Why is my face and one eyelid swelling during heavy exercise?

Fluid changes. The tissues around the eyelids swell very easily. Exercise increases blood flow to the face and causes you to strain. This could result in some swelling of the eyelids.

Related Questions

Why is my face and one eyelid swelling during intense exercise?

Urticaria? One possibility is exercise related urticaria. A sort of "allergy" to exercise. Ask our ophthalmologists so they can rule out other local or systemic disorders.
Venous obstruction. This could be a sign of venous obstruction aggravated by intense internal pressure generated by the excersize. See your family doc first.