What does "drop" mean in this context?

Solution 1:

Is this the dictionary definition that comes the closest to the usage in that Meta post?

No, the dictionary definition that comes closest is 1b in the same Merriam-Webster entry:

a minute quantity or degree of something nonmaterial or intangible

So when Sara Chipps elaborated “a drop” on why, she only explained the reasons “a little bit”, “to a small degree”, ever so “slightly”, “a tad”.

Solution 2:

Considering in the same link the person says, "possibly a drop longer", a synonym for "drop" in both cases that's makes sense is "bit", meaning a small amount. Drop can be found to be a synonym of bit in some online references.

https://www.thesaurus.com/browse/drop

Solution 3:

Recently, it was announced that the "Hot on Meta" questions would no longer show up on the SO sidebar. Sara Chipps elaborated a drop on why:

From context, the meaning appears to be akin to an 'information drop' - either a guess or actual cause. Perhaps the term was off-the-cuff, or even shorthand from a particular occupation.

Edit: After seeing the thread, I now agree that the most likely candidate is "a bit", a small amount.