A: What's the weather doing?
B: It's raining. — Herg

A: What's the bumble bee doing?
B: It's raining.

So "it" refers to the bumble bee.

The conversation makes no sense, but the syntactic connection is sound. In your conversation "it" refers to the weather; in mine to the bumble bee. But it's a question of syntax, not semantics.

Does it matter that your conversation makes sense and mine doesn't, for determining reference?

A: What's the bumble bee doing?
B: It's raining.

So "it" refers to the bumble bee.

The conversation makes no sense, but the syntactic connection is sound. In your conversation "it" refers to the weather; in mine to the bumble bee. But it's a question of syntax, not semantics.

Does it matter that your conversation makes sense and mine doesn't, for determining reference? — Dawnstorm

There are two possible readings of your "B: It's raining.", as follows:
1. 'It' refers to the bumble bee. In this case, since a bumble bee can't rain, the speaker is uttering nonsense.
2. (much more likely in real life) 'It' refers to the weather, and B is not answering A at all.

So semantics matters. You can't simply assume that in 'it's raining', 'it' refers to the subject of the most recent sentence uttered. As Terrapin Station has said, 'it' is indexical, and in any sentence about the weather, suich as 'it is raining' or 'it is sunny', 'it' refers to the weather.

There are two possible readings of your "B: It's raining.", as follows:
1. 'It' refers to the bumble bee. In this case, since a bumble bee can't rain, the speaker is uttering nonsense.
2. (much more likely in real life) 'It' refers to the weather, and B is not answering A at all.

So semantics matters. You can't simply assume that in 'it's raining', 'it' refers to the subject of the most recent sentence uttered. As Terrapin Station has said, 'it' is indexical, and in any sentence about the weather, suich as 'it is raining' or 'it is sunny', 'it' refers to the weather. — Herg

I could say the same thing about your example. Maybe B didn't hear what A was saying, and is just commenting about the weather, the connection being a co-incidence.

Your example proves nothing, because you're basing the proof on the same imputed connection that I did in this example. But if the connection is there, you have anaphoric it and not dummy it. It's not the same situation.

A: What's the weather doing?
B: It's raining.

Assumption 1: B responds to A. Anaphoric it.
Assumption 2: B ignores A, and is randomly commenting on the weather. Dummy it.

Two different situations. It's just more obvious with the bumble bee example.

You can err on any utterance; but that's a question for pragmatics or conversation analysis rather than either syntax or semantics.

Yeah, context matters. But it matters on more than one level, and you have to be careful not to mix them up.

'it' is indexical, and in any sentence about the weather, 'it is raining' or 'it is sunny', 'it' refers to the weather. — Herg

You're mixing up your forms like Terrapin did.

The "it" in "it is raining" cannot syntactically refer to the weather in the trivial way the "it" does in "it is sunny" because the syntax differs. This is made obvious when you consider that "a sunny day" is a correct form but "a raining day" isn't. The day can be "sunny" but the day cannot be "raining". Rather, it can be rainy.

So, the proper syntactical parallels are:

It (regular pronoun indexing the weather) is sunny (adjective). ✓
It (regular pronoun indexing the weather) is rainy (adjective). ✓

and

It (dummy pronoun with no clear referent) is raining (present participle). ✓
It (dummy pronoun with no clear referent) is sunning (present participle). X*

*But we can say "She is sunning herself" meaning sunbathing. The reflexive version seems to have stolen the opportunity for a non-reflexive parallel to "It is raining". So, why the difference? Maybe because of the different characteristics of each phenomena (we lie in the sun not in the rain and the rain falling seems more active and verb-like than the emission of less tangible light rays) or maybe because of some etymological accident. Fact remains, the former is valid and the latter isn't, and the most straightforward and commonly accepted logical analysis of the former is the non-indexical dummy pronoun angle, the objections given in this discussion so far having being based on misunderstandings.

Not every language expresses the idea of 'it's raining" intransitively the same way English does, as at least @Hanover has also pointed out. For example, in Ukrainian the standard phrase is "Dosht' padaje" which translates literally to "rain falls" or "rain is falling". There is no question about what the subject is because its "rain," even though it conveys the exact same meaning or propositional content as its English translation.

Alternatively, in Latin for example, the verb is "pluit" where the subject is marked by the conjugational ending. In language like that, there isn't even a way to ask what the syntactic subject refers to because it is built into the verb itself. It would not raise any more question than the statement "currit" meaning "he/she/it runs". It might invite the question "quis currit?" - "who runs?" - but the sentence as it stand nevertheless conveys meaning. If analogously one were to ask "quid pluit?" - "what rains?", I suppose the answer would be "pluvia pluit" - "the rain rains". That seems like a plausible enough answer in the case of English as well: the "it" just refers to the intransitive (NOT reflexive) activity of the rain itself.

You could also just treat the whole sentence "it is raining" as paraphrase for a sentence with identical meaning where the subject is explicit and unproblematic. For example, it would be shorthand for the semantically equivalent "rain is failing", "rain is happening now" or whatever. There's no point in asking about the meaning of "it" in isolation because it has none independently of its functional role in the sentence as a whole. And what that sentence means is given by whatever truth conditions make it true or false. Those truth conditions, in turn, don't depend on whatever form we choose to express those conditions in within a language, making it arbitrary to prefer one form, e.g. "it's raining", to another, e.g. "rain falls".

The "it" in "it is raining" cannot syntactically refer to the weather in the trivial way the "it" does in "it is sunny" because the syntax differs. — Baden

In the exchange Herg provided (What's the weather doing?/It's raining.) it can. People may consider it awkward, but "it is raining," as an analogue to "the weather is raining," as a reply to "what is the weather doing?" is plausible (but not necessary; it's ultimately an empirical question - I do agree with Terrapin Station that it's all in the head).

The conversation says nothing about dummy it, though, other than in the case of a plausible antecedant for "it" a sentence might be ambiguous between dummy it and anaphoric it.

The "it" in "it is raining" cannot syntactically refer to the weather in the trivial way the "it" does in "it is sunny" because the syntax differs. This is made obvious when you consider that "a sunny day" is a correct form but "a raining day" isn't. The day can be "sunny" but the day cannot be "raining". Rather, it can be rainy. — Baden

But you have changed 'weather' to 'day' here, and so you're attacking a straw man.

the most straightforward and commonly accepted logical analysis of the former is the non-indexical dummy pronoun angle, — Baden

To me this seems rather less straightforward than the view that "it" in "it is raining" refers to something. I suggest that what has actually happened here is that what it refers to (the weather) is no longer overtly mentioned because it is almost always the weather, and nothing else, that is raining, and so there's usually no need to mention the weather explicitly.

Merriam-Webster (https://www.merriam-webster.com/dictionary/rain) offers three definitions of 'rain' as an intransitive verb:
"1 : to send down rain
2 : to fall as water in drops from the clouds
3 : to fall like rain"

In the exchange I offered, because "it is raining" is given as an answer to the question "what's the weather doing?", the appropriate definition is 1, i.e:
A: What's the weather doing?
B: It's raining (= sending down rain).

It is also possible to have this exchange:
A: What's the rain doing?
B: It's raining.
B has uttered a trivial truth. A may be annoyed with B for uttering it, but then A has only himself to blame for asking such a silly question (what would the rain be doing, after all?). In this exchange, the relevant definition of 'rain' from Merriam-Webster is 2, i.e.;
A: What's the rain doing?
B: It's raining (= falling as water in drops from the clouds).
This is also the sense of the verb in unenlightened's quoted verse by Charles Bowen ("The rain it raineth on the just") and also, incidentally, by Shakespeare, in the Fool's song from 'Twelfth Night' ("For the rain it raineth every day").

Usually when someone says "it is raining", they intend to be informative, and not merely utter a trivial truth. What they intend to inform us about is the weather, so I think it is reasonable to conclude that the "it" in "it is raining" usually refers to the weather, and that the relevant definition of the verb is Merriam-Webster's 1.

But you have changed 'weather' to 'day' here, and so you're attacking a straw man. — Herg

Sunny day, rainy day. Sunny weather, rainy weather. Get it now?

It is also possible to have this exchange:
A: What's the rain doing?
B: It's raining. — Herg

Never heard that one. Although "what's the weather doing" was new to me too and that apparently is a thing, so food for thought.

incidentally, by Shakespeare, in the Fool's song from 'Twelfth Night' ("For the rain it raineth every day"). — Herg

Love Shakespeare's use of language. "But me no buts" is one of my favourites.

Or as @Banno might say, silliness sillying. Unless you're a grammar nerd like me.

"It's raining men, Hallelujah!"

Strange weather days.

The "it" in "it is raining" cannot syntactically refer — Baden

Syntax by itself doesn't refer. And reference is semantics. Reference requires thinking. What refers, and the way it refers, is purely a matter of how an individual thinks about it.

What refers, and the way it refers, is purely a matter of how an individual thinks about it. — Terrapin Station

Which of course means, "I'm not talking to you, I'm talking to myself."

Communication doesn't hinge on syntax referring or on reference being something non-mental.

Communication doesn't hinge on syntax referring or on reference being something non-mental. — Terrapin Station

Which of course means, "I'm not talking to you, I'm talking to myself."

Aren't we not supposed to be trolling on this board?

the lower layers of the atmosphere in the locality. As for the real causal agent, the Universe and its entropy.

Aren't we not supposed to be trolling on this board? — Terrapin Station

Which means, "I can't even deny it according to my own theory."