I can gain weight at 250 miles a week if I do not watch what I eat. Cardio is a needed piece but your nutrition is as important. Right now I am eating reasonably and riding roughly 100 miles a week and loosing about a lb a week. However, I am also not just riding at my cruising speed but following a training plan as well. One day intervals, the next a slower speed base mile ride, and so on.
One can loose weight at 50 miles a week. Just watch your nutrition and make those miles count. However, it may be easier with more miles.
My two cents.