What you describe is a common symptom of sleep apnea. Snoring, made worse by even slight weight gain, with progression into breathing pauses, is a typical symptom of sleep apnea.
Poor sleep can aggravate weight gain, and weight gain aggravates sleep apnea. You don't have to even snore or be overweight to have significant obstructive sleep apnea. Some of the other common symptoms of sleep apnea include: chronic daytime fatigue or drowsiness, inability to focus or concentrate, headaches, sinus pain and pressure, poor digestion, frequent trips to the bathroom, and nasal congestion. Untreated sleep apnea can cause or aggravate anxiety, depression, hypertension, diabetes, heart disease, heart attack, stroke, kidney failure, seizures, impotence, car accidents, and early death for any reason.
The best way to find out what's going on is to see a sleep doctor and to undergo a formal sleep study.