Hi groundhog - you burn calories by doing exercise and therefore you can eat more and stay the same weight.
Also if you do exercise that builds muscle - this increases your resting metabolism which means you burn more calories even if doing nothing. Swimming may well help to build muscle (arms?), and cycling (legs) but some sort of body conditioning/toning will also help.
Therefore I would suggest a combination of something that raises your heart rate (cardiovascular) - walking, swimming or cycling etc, along with some sort of muscle toning - class or gym.
Hurdity x