So when I looked at constitution I wanted to look for a way to make it useful but not hand out mounds of hit points. Put simply constitution can help you heal up and come back from a fight but not survive a hit from a bazooka. It will let you shrug off the effects of non-fatal injuries.
Low: (still within human levels but nearly immune to pain and minor injuries.. Think Rasputin). The character gets an advantage die when making a constitution save of course. He requires half the sleep, half the food and is considered to roll maximum for hit points every level (18 hit points if you go by constitution equals hit points and double if you figure hit points = level).
Paranormal: (not within human limits. Think comic book villains who seem to suffer certain death and yet return). The character gets an advantage die when making a constitution save. Hit points are figured as for the previous power level. In addition the character gets 1d8 hit points back after a combat twice a day (or 3 times a day if they are combat class.) The character needs one quarter the sleep, food, and water of a normal human and can get by on these reduced levels for at least a week.
As an alternative to rolling with advantage super constitution can subtract from saves: -2/-4/-8 depending on level.