There are a few exceptions to the rule that your sim does nothing but show up on community lots or as walkbys. One is university, if you rotate during a term your sim will finish the term without you. Your households will also vote in NAPs if there are slots in their neighborhood and you don't turn it off. And with the new neighborhood stories feature he might call the other sim you are playing to ask for advice but you can always say no to the ones you don't want for him.
I have never had a problem with random flirting between background Sims, but they do try to flirt with my active Sims if they aren't related on occasion. The weight gain thing is definitely something you'll need to address if you go to public lots often, either with a mod or by fixing it when you rotate back.