if you train for a marathon you can run a marathon. it's that simple. Doesn't matter if you're thin or overweight.
And again, not everyone in your Squad has to be the hard ass special ops recon uber Marine type of guy. Who knows what will go on on the Ark but I'm sure it's not gonna be filled with 100% military.
Your weight does matter if you're going to run a marathon and actually finish well, without walking a portion of it. You're right that training could prepare a person, but then if an overweight person was seriously training to run a marathon they'd end up losing weight.
I agree about the Ark, but the protagonist and their squad are going to be doing similar sorts of activities as military personnel, even if they aren't military personnel themselves. Its worth noting that there are also physical fitness requirements for being an astronaut. The protagonist or a squadmate being obese would stretch suspension of disbelief a bit.
That isn't to say that people can't ask for obese squadmates or obese options for the player character in the CC, but I think that argument has to made on the basis of representation being more important than realism. I'd disagree, but I'd understand that viewpoint. Any argument that an obese squadmate or protagonist would not be far-fetched however, I think has less weight behind it. It's just a reality that some jobs can't be performed adequately unless you have some degree of physical fitness.