1
He does more exercise because he is putting on weight.
He does more exercise because of putting on weight.
He is putting on weight, so he does more exercise.
2. 
He stayed at home because he was sick.
He stayed at home because of being sick.
He was sick, so he stayed at home.
3.
It was very cold, but they went swimming.
It was very cold. However, they went swimming.
Though it was very cold, they went swimming.
Despite the fact that it was very cold, they went swimming.