You have not specified where is this heaviness? Head, chest, feet, or elsewhere.
I presume it's chest heaviness. Then we must rule out angina pectoris.
Next Steps
Get an ECG, and a stress test ( stress echo/ TMT) on under supervision.
Health Tips
Avoid exertion that produces chest heaviness.
Get thorough evaluation.
Diabetic cases are also known to have silent heart attack. So don't take things lightly.