Most people are under the delusion that when they lose a pound, it's all fat. In reality, especially for someone whose main exercise is an endurance activity like cycling, 75% of that weight loss can be muscle. This gets the thighs slimmer, sure, but often primes us for fat gain when the metabolism decreases as well. And like you have witnessed, leads to strength losses.
*everyone* benefits from weight training. It can be the deciding factor in your goal to keep as much muscle as possible. You also need to make sure you have your post-exercise nutrition in order, and start keeping a log of every calorie that goes in your mouth for the next few months to make sure you're getting adequate calories and protein. Those are probably the best things you can do to stem the tide.
Good job on the fat loss, though!