Let me ask you, then: who should this woman have cosplayed, that would have fit her body type?

It's hard to say. Similar with the situation of black people, there aren't that many video game characters (or anime characters) that match.

The reasons for this are pretty obviously tied to our cultural conceptions of beauty—women should be slender and curvy. There's obviously some exceptions, but most are still of a pretty average build.

I definitely agree. I never said otherwise. Some characters are quite impossible to cosplay accurately, no matter who you are.

Should she be disallowed from the hobby, or ridiculed for doing something she enjoys, just for this?

I never said disallowed. Nor did I say that she should be shamed/ridiculed. I mentioned this in my post. I'm supportive of people dressing how they want to dress. That's not the issue. The issue is that cosplay (to me at least) implies you are trying to be that character. Hence dressing as them and (in extreme cases) role playing them. The more differences there are between you and that character, the more you have failed. And people should note this when they do cosplay. Because there are people who will ridicule them. There shouldn't be, but there is.

Honestly, I'm even disgusted when thin people cosplay fat characters and then get applause and cheered on. Or when the details of the costume are off (person is holding the sword in their right hand for a left handed character). Detail matters. Even if it is something that people find sensitive about themselves (weight, skin color, etc).

Additionally, I know a fair number of cosplayers choose the characters they do because they identify with the character's struggles and characteristics, and not solely because they look cool.

That's fine. That in some cases may improve the cosplay. But that's impossible to tell from a picture.

Caitlin describes Lara Croft as "feminine but dangerous, well-educated but athletic". By dressing as her, becoming her, she's taking on some of those traits. If it boosts her morale, if it makes her feel better about herself, because she is sees herself in that way, or is acting in that manner, why should she let her weight and build be a barrier to positive mental health?

As I said. Dressing as her is fine. I never said otherwise. I said that it was poor cosplay when she did so. And her weight was the main factor.

To provide another example of a failed cosplay (not related to weight) is this guy here:

He was trying to cosplay this character:

Compare that to this fellow:

The second guy clearly did the cosplay better (even if it's not perfect). And barret wallace (the character being cosplayed) is basically impossible to get the body type right. I've personally never seen anyone with that shape/height/mass except for maybe one guy. In my entire life.

The point is, both people are free to cosplay as him. But don't be sad/mad/angry/upset when people say your costume is inferior.

Hate speech is definitely too far, but just because a person is insecure about how they look, doesn't mean their cosplay is immune to being critiqued and criticized.