It very definitely can.  We all know it’s not supposed to, but it’s hard for an interviewer not to shift into instant first impressions in line with the fat stereotype, even if they are themselves obese.

So you may be immediately classified as out of control, undisciplined, lazy, and someone who’s going to spend a lot of time eating.

Even if this isn’t the case, if you’re tied with another contestant for the job and that person is like you in every way but they’re in great physical shape, they may be classified as being more of a disciplined, self-aware, self-controlled person, a real go-getter, someone the boss could take into customer meetings knowing they’d make a good impression.  Maybe the comparison is not as straightforward, it may add only 1% to the impression you give, but that 1% may easily be enough to tip the scales in their favor.