It's a factor, probably not as much as they used to think it was. I listen to Dr. Peter Attia podcast interviews with cardiologist and other researchers on cholesterol and it's so much more complicated than the 4 numbers (HDL, LDL, Triglycerides, Total) most people monitor. I have a friend with very good numbers who's on a keto diet. He eats eggs, nuts and animal fats freely. In a recent episode Dr. Attia said that we may have been overlooking the major effects of stress on cardiac health and it might outweigh diet as a factor.
Excess weight does add to your risk of heart attack and puts a strain on your heart, your hips, your back....Pick up a 20-lb. child and walk upstairs carrying them and tell me you don't feel anything. Now imagine doing that all day.
I'm 70 and I've also got shortness of breath and do everything "right"- BMI under 20, over an hour of low-impact cardio every day, rarely eat meat, low BP (no effort in my part- it just is). I passed a treadmill test with flying colors and my calcium score was 1. I have mitral valve regurgitation and my cardiologist tells me it's a Stuff Happens thing- nothing I did.
You really need to change the things you can, and keep an eye on the whole picture.