A lot of games do leveling up by just increasing the value that is most used, i.e. using a weapon improves your marksmanship, close combat fighting improves your strength and well, getting hit a lot improves health.
I would combine this generic leveling with only few extra points that boost your skills (not general things like strength, agility, perception, health) like lockpicking, stealth, defusing bombs, repairing items etc