I did the same, went on a low carb diet, lost 22 pounds (I'm not a large man, under 5' 9", so that was a chunk o' weight for me), but I have been active on my feet for decades. I still walked or ran for between 10-22 km each day, or maybe five days each week. So, I can vouch for changing habits as a potential cure for heart problems.

However, it was really the undiagnosed sleep apnea that was most of the problem for me. Weight, yes, and the cardiologist I saw about my fibrillating heart put me on metoprolol for two reasons: incipient hypertension and to control my rapid atrial firing when my heart decided it was cranky enough to want to fibrillate. The problem, the trigger, for the cranky heart, though, was sleep apnea. In my case, the polysomnography results was a devastating 'severe obstructive sleep apnea.' And I couldn't be called 'overweight' back when this happened....the weight gain came subsequently when I felt I couldn't risk taxing my heart with aerobic running.