usually with "barely" you wanna keep it close to the verb, so "you felt like you could barely breathe" or maybe "you barely felt like you could breathe" sounds better than "you could barely feel like you could breathe". The double 'could' and the positioning of 'barely' makes it sound like a double hypothetical.

I would change "other gross people" to make it clear that 'you' is not intended to be gross. If it is intended to be gross, I'd make it more explicit, like "surrounded by other gross, sweaty people... well, you were gross and sweaty too, but that's not the point." or something like that.

I think the "catch up" line in the back and forth is confusing, it took me 2-3 reads before I realized you were not talking about intentionally catching up in weight, but rather like, keeping up with them. I would try a phrasing like that, like "if you lost some weight they wouldn't get away from you so easy" or something like that.

"far-jutting" is a little loose, it's like "big belly". not bad, but it could be more concrete. Something like "hips the width of a personal hovercar and a rear end to match" even would read more firmly to me, like it's pretty clear her ass is also as big as a car, without leaving me to wonder how much "far-jutting" is.

Semicolon after "to match", rather than colon. Could also use an em-dash (I do this too much...)

Should use the subjunctive to make it more clear it's a hypothetical: "Even if you hadn't followed her to the precinct after graduating from the Academy, you'd (probably) still be stuck together."

"the film of synth-perspirant she's covered in doesn't seem to be helping" -- helping what? the MC's horniness? how hot she is? The former doesn't seem to be sold hard enough (you should include more lines about how she makes you crazy, or something) and the latter doesn't really make sense to me (perspiration is supposed to cool you off). I get the literal nature of "doesn't seem to be helping", but then the question is why even have it, and... Anyway I dunno, up to you.

"thump" could use some more descriptors, like "A thud like a refrigerator slamming against the floor", or I don't know. Even just "a heavy thud" would pull the sentence together. On the flip side I do appreciate that you don't litter your prose with tons of useless adjectives, but here it feels appropriate.

Not sure I get what you're going for with the line about provisions. Like this provision is supposed to make it legal for 600+ lb citizens to go naked or something? The previous line is fine, but I don't get what this is implying. Could be made a little more clear IMO.

some of this is taste but I really do not like exclamation points in narration, and the "her favorite flavor!" one feels like it just reads better without it. Sounds more matter of fact.

I would change "of one five-liter tank" to "the first five-liter tank". I had to re-read the sentence because by the time I got to the end I wasn't sure what "the second" was referring to anymore (admittedly this is partially because I'm stopping to give critique, but still, 'first' is good because it implies a second, which 'one' doesn't necessarily).

"megafrat" definitely comes across as an attempt at a neologism a la newspeak or overtrain but I'm not sure it lands as well. Maybe you could jazz that up, like 'robofrat' or something silly?

"her gut enters a bit before she does" is good but again could be emphasized a little harder. Something like "you notice how her belly clears a full step before she does, bouncing weightily with her waddling gait", or anything to just pause on that moment a little longer.

some of the tone is a little inconsistent to me, like "dolt" reads very high class and haughty, but then you have "they gotta sextuple their rations!!!" from the same character, which reads super giggly tumblr girl-ish. up to you here, i don't know the full image of the character you've got but that's how it reads to me here.

"elicit" not "illicit". Also I would treat "protest" as a countable noun, as in "elicit a creaking protest(ation)".

the ending is good, I think it sells the vignette well.