You don't necessarily get 'fitter' by losing weight alone although you feel so much better for not carting the excess bulk about. That in turn makes you WANT to move about more so might help you get a bit fitter. To really capitalise on the fitness thing though, some sort of proper exercise is needed. It doesn't have to be a gym; it could be walking, cycling, swimming, ice-skating etc. Doing a programme of resistance exercise (weights) helps build (tone) the muscle that burns the fat and it improves shape.
PS
Moderate exercise is OK on SS but you shouldn't do intensive cardio workouts
