Why did many Southern states once ban incumbent governors from serving back to back terms?

[Greedo punched first]

Virginia is currently the only state like this. Alabama and Mississippi use to be like that. What was the reason for this?

[Skill and Chance]

Extreme fear of executive power during the early republic era.   Almost of the states with simple majority veto overrides (AR, AL, IN, KY, TN, WV) are also Southern or heavily Southern influenced, and NC, MD, and DE have a 60% override threshold instead of the standard 2/3rds.  NC only introduced the gubernatorial veto at all in the 1990's.