Chewing gum while working out?
It's a little weird, and could possibly be a bad habit if it affects
your breathing. Getting sufficient oxygen to your lungs while you work
out is important, so if that is in anyway affecting that, then I would
cut it out.
But honestly, you should be working out at a level where gum-chewing is
not possible because your breathing too hard. Sounds like your kind of
taking it easy at the gym. Push yourself if you really want to see
results.