I'm 5'3 and a hair under 130 and don't have a beer gut. I don't know how accurate is but my scale says I'm around 15-16% body fat. I lift weights but I can't imagine I have more muscle mass than someone working as a mechanic and cycling. OPs numbers don't add up to me either.
After other comments that might be it. Though I've been sober for over a decade now (never had a problem with drinking, just not my thing and lost friend and family to it so I don't do it)
It's just the most common way ppl get it. If you eat lots of carbs, you can develop it. It's not a drastic change, but 10 years of rice, bread, pasta, etc will catch up with you. Get checked out by a doc to rule out glands and hormones as well.
130 pounds is pretty low for a man your height. Considering you've never really worked out, do some body weight workouts on YouTube, or but some dumbbells and do the same. Start with 20 pounds and but heavier as you need.
You lose weight with diet, not exercise, but that's not what you need.
For reference 159 pounds would be where you start to cross into an 'unhealthy' BMI. However, while BMI is a good gauge for normal/sedintary people, it isn't a great measure if you're quite muscular. So I would try to stay under 160 unless you've been building miserable consistently for 1-2 years. And even then, if you are trying to optimize health, no need to go much over, even 160 being swole. However if your primary goal is not health but strength, you'll need to be 'obese'. Which is still healthier than being thin and out of shape, but not 'optimal' for long term health. The reason I say this is, everyone has an opinion on what's best, but it really depends on what you're trying to optimize for.