Is peripheral artery disease correlated with pain and heaviness in your legs?

Potentially yes: Peripheral vascular disease causes three levels of symptoms as the disease progresses, 1) claudication; muscle cramping with exercise which also resolves with rest. This is very reproducible 2) rest pain; pain when elevating legs / lying down, 3) tissue loss; foot ulcers / gangrene / non-healing wounds. Pain and numbness are more frequent than heaviness.

Yes: Pad can cause this but venous insufficiency can also. Better get checked.

Don't forget veins: As dr. Aalami said, heaviness is unusual and in my experience is more likely to be associated with venous insufficiency. I agree with dr. Korna, it is worth checking it out to make sure that veins aren't the cause of the problem.