2005 Chevy Equinox keeps blowing back up fuse. Why?

Something is shorted and drawing too much current. Try installing a pair of spade terminals in place of the fuse, then connect two small jumper wires to them and to a 12 volt light bulb. The bulb will limit current to a safe value and will simply be full brightness when the short is present and the circuit is turned on. Now you can unplug, wiggle, and reposition stuff to see what makes the bulb dim or go out. When it does, you removed the short.

If the bulb is bright as soon as you turn on the ignition switch, suspect a shorted backup light switch but that isn't common anymore since the insane engineers use the switch to turn on a circuit in a computer which runs the backup lights. Quite the Rube Goldberg system but that's what all manufacturers are doing now.

If the bulb doesn't get bright until you shift into reverse, the short is in the wiring going to the rear lights. If a trailer harness was added, check behind the tail light housing for a pinched wire that finally rubbed through and is grounded.

A bad ground will not caused it to blow a fuse-the short has to be in the wiring before and after the B/U switch or the switch itself. A bad ground will caused it not to come on not to blow a fuse at the same time-