Bottom line it's personal preference. If the weight of the tailgate significantly impacts your rig you got bigger problems. I leave the gate on my Dodge to help the unsupported length of the camper overhang. Also had no choice since the first trip with the camper was a move to Alaska and didn't feel like not having the tailgate for 2 years!
In short, it doesn't matter but I'd rather support the back of the camper