Noemon: There's no relation. Cover is from the French cuvrir, which comes from the Latin cooperire, from the intensive prefix com + operire, meaning 'to close or cover'.
Over comes from the Proto-Germanic *uberi, which ultimately comes from the Proto-Indo-European *uper. The Latin super and Greek hyper come from the same root, though I don't know where the s comes from. (Greek words with h often come from PIE words with s; compare Latin sex and sept and Greek hex and hept.)
Interestingly, *uper is the comparative form of *upo, meaning 'under' or 'up from below'. *Upo is the source of sub, hypo, and up.