If you can isolate the area where you feel the pain and pain increases when you press the area, it probably isn't your heart. You are at the age where both arthritis and acid reflex are issues. Does the discomfort decrease when you take an anti-inflammatory or an anti-acid product?
I'd doubt that fat is the problem. Maybe others have information about that, but I've never heard of that being an issue, you aren't that far outside the BMI range. Best wishes.
Sounds more like acid reflex. Try using Prilosec, if you can, for 2 weeks to see if it goes away. If it does, then you know it was your stomach.