Yes formula does make babies fat if they're fed formula more than breastmilk.
Sometimes that's a good thing when the baby needs to gain weight and other times it may not be a good thing but it has been shown that babies who're formula fed do tend to gain more weight than breastfed babies.
Breast Milk is always the best milk for the baby though when you can supply them breast milk however feeding your baby formula instead is still okay.
But if you do notice your baby getting too fat from the formula then you might want to switch over to breast milk instead if possible.
If you're able to produce breast milk for your baby then it would be a good idea to feed the baby some breast milk along with the formula as you'll have a much healthier baby as a result.