First of all, whenever the period stops suddenly it is of course necessary to make sure that it is not from a pregnancy. It sounds like you have probably considered this possibility already, but if not, the first step would be a pregnancy test.
You should also get a medical evaluation to get to the bottom of the issue. The best option would probably be to see an OB GYN doctor
at your earliest convenience.
One of the most common reasons for irregular or missing periods is something called polycystic ovarian syndrome. This is an extremely common medical condition, caused by an imbalance in hormone levels that periodically results in failure of ovulation. The condition is definitely associated with being overweight, so that could also be related.
Another condition which can cause missed periods and weight gain is hypothyroidism, which involves an under active thyroid gland and not enough circulating thyroid hormones in the blood stream.
Your doctor will be able to perform a thorough medical examination looking for these and other causes. They will probably also want to get some basic blood work to make sure that checks out.
Make an OB GYN appointment as soon as you can!