In the process of losing weight, women usually consume fewer calories. Lower food intake leads to lower blood sugar levels. With lower blood sugar levels, the ovaries become less active. Unlike most other tissues in the body, the ovaries cannot resist the effects of insulin. If blood sugar levels are high, the ovaries will be flooded with glucose, and the only thing they can do with all the glucose is to become more active. The ovaries make estrogen, but they also make testosterone. It's the additional testosterone that interferes with fertility. Even when there is not enough testosterone to cause unwanted hair growth, acne, or male-pattern baldness without being male, there can be enough to testosterone to interfere with ovulation.
It's not so much what women weigh that makes the difference, as it is that the process of losing the weight that brings blood sugar levels down and stops the overproduction of testosterone. Some men with fertility issues also benefit from losing weight. Men with obstructive azoospermia, for example, usually have "plumbing issues" trapping sperm in the testes. If the problem is pressure from the renal vein that is in turn placing pressure on the veins that supply the testicles, then 2 to 20 pounds of weight loss, if otherwise indicated, can increase sperm counts.
When the issue is non-obstructive azoospermia related to low testosterone levels, weight loss may also be helpful. Shrinking fat cells will not increase testosterone levels directly, but it will decrease estrogen production, since fat cells make estrogen. Simply shifting the ratio of estrogen to testosterone sometimes enhances fertility. Weight loss, of course, is just one too of getting pregnant fast naturally. Changes in sexual position, common and safe nutritional supplements and herbs, also often help.