If by FATES you mean FATE, I can't really think of anything else that is less rules intensive. One combat there lasts approximately 10 minutes (if the players make decision of what I want to do quickly) up to about 30. Only systems I know of that are lighter are the ones that barely have any rules at all, like Window or this one TTRPG that could be played with a napkin with stickman drawn on it. Their problem is that they completely lack mechanical depth.

Maybe look up FATE Accelerated, I wasn't a fan of it because it offered little choice when it came to combat, but it could work for RP-heavy, fight-light game. Also remember that FATE, whether Core or Accelerated, have a lot of optional rules listed (weapons and armor with shifts are the most visible), take those out and you basically have a "roll your skill against other skill" system with two sets of hitpoints.