T should cause an increase in muscle mass and strength. Muscle weighs more than fat. Muscle cells also burn calories all the time, even while asleep, whereas fat cells only burn calories while you're active. In that sense, yes, it should increase your metabolism.
In short, weight gain should not be surprising and should not (automatically) be interpreted as a bad thing, health-wise. Men, in general, certainly weigh more than women. If you really don't want an increase in muscle mass, you might want to talk to your doctor about T and whether you want to go on it.