Can you re-equip equipment to the same creature?
Yes, you can choose the currently equipped creature to target with the equip ability since it doesn't require the target to be a different creature.

Note that if you have other cards that care about things becoming (un)equipped or (un)attached they will not trigger since the equipment never actually stops being equipped, and it doesn't gain a new timestamp.


  702.6a Equip is an activated ability of Equipment cards. “Equip [cost]” means “[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery.”