Why might it be that my eyes feel so heavy when wearing my contacts?

Possibly not fitting: A heavy feeling when wearing contact lenses can be from the lenses fitting too tightly. As a result the contacts move very little on the surface of the eye, and the cornea can begin to swell, which tightens the fit even more. Dryness also can feel this way. Talk to the doctor who prescribed the lenses to possibly check the fit or see if something else is going on.

Dry/ allergy: Get an eye exam. You may just have dry eyes, and contact friendly artificial tears may help lessen this feeling. Also lessening your wear time too may help. More importantly, you may have a contact lens associated allergy (gpc), that requires treatment. An eye md would help you with this.