I don't mean to be discriminatory, but if a person can't physically care for themselves, I don't think it's a good idea for them to care for a baby. Especially if they don't have a partner that can carry the slack. Now I'm not advocating taking away a person's biological child without solid proof of neglect, but for adoption I think it's totally reasonable to look at if they are able to take care of a kid and turn them down if they can't.
Being a little overweight or obese is unlikely to cause major issues, but Whitney in particular is far beyond that. Just on the show alone we've seen so many instances of relying on other people to put on shoes, shave her legs, put on ointment, help her out of the shower, pull her up from ski's, etc. There's no way she could adequately care for an active toddler.
It doesn't really matter, because like the pregnancy storyline a few seasons ago I'm pretty sure this is all just for show and will get completely dropped after a few episodes.