Why does my right leg feel really heavy?

Be seen: It could be a couple of serious conditions, including a DVT or even a stroke.

Swelling: Swelling can cause a feeling of heaviness as the day goes on. The question would be what is the cause of the swelling.Check with a medical doctor.

Heavy leg: there are many possible sources for this feeling. From a vascular standpoint I would recommend a venous Doppler sonogram to determine if venous reflux, and varicose veins are the source of this feeling. As the vein blood flow refluxes down the leg there is an increase in volume which may cause the leg to feel heavy.