Sorry it took me so long to respond; I had to find my copy of The Elements of Style by Strunk Jr. and E.B. White. Here is a relevant quote from that excellent style guide:

If two or more clauses grammatically complete and not joined by a conjunction are to form a single compound sentence, the proper mark of punctuation is a semicolon.

Mary Shelley’s works are entertaining; they are full of engaging ideas.

[…vs.]

Mary Shelley’s works are entertaining. They are full of engaging ideas.

[…vs.]

Mary Shelley’s works are entertaining, for they are full of engaging ideas.

[…] A comparison of the three forms given above will show clearly the advantage of the first. It is, at least in the examples given, better than the second form because it suggests the close relationship between the two statements in a way that the second does not attempt, and better than the third because it is briefer and therefore more forcible. […]

Note that if the second clause is preceded by an adverb, such as accordingly, besides, then, therefore, or thus, and not by a conjunction, the semicolon is still required.

I had never been in the place before; besides, it was dark as a tomb.

Alright, back to me. A good example of what I’m referring to with “weight” is revealed when discussing how to properly use a semicolon with an ordinary colon. A semicolon is “heavier” than a colon; let me give you an example to illustrate this.

The answer: humanity is doomed; the people are angry.

This is stylisticly bad, because the semicolon separates the clause “the people are angry” from the context (the scope, if you’re a programmer) of the colon: now the clause is equal to the rest of the sentence, “The answer: humanity is doomed,” instead of serving as part of the clause “The answer:” is describing. The correct—that is, the intended—sentence would simply be this:

The answer: humanity is doomed, the people are angry.

One might think that this is illegal, as there is no conjunction, but, indeed, that presumption would be incorrect: “[…] humanity is doomed, the people are angry” is actually a list and the author of the sentence (me, muahahahaha) is using a literary device called asyndeton.

Here’s an example of asyndeton:

The ingredients of despair: hope, yearning, jealousy, conjecture.

The incorrect version would be with a semicolon introducing the last element of the list.

The ingredients of despair: hope, yearning, jealousy; conjecture.

Because the first example has only two elements, it can seem like one has to use a semicolon, but I think that the example given above shows how that is, in reality, quite absurd.

Alright, rant over, I hope this has sufficiently answered your question! Have a good day :)