Is eyelids revision just for cosmetic reasons or will it also help them to work right?

Both. Eyelid surgery can have different goals: correct extra skin, remove extra fat, reposition the levator muscle, shorten muscles, reposition the corners and many more options. It all depends what do your eyelids need to be done to them. That is why you need a thorough evaluation and eye exam prior to surgery.
Indications? It really depends on the indications for surgery and underlying anatomy and function. For example, drooping upper eyelid skin (dermstochalasis) may interfere with vision by covering the pupil. If the ski. Is removed both cosmetic and functional imporvement will be accomplished. However certain conditions such as lower eyelid fat may be more purely cosmetic.
Should improve. The removal of the excess skin in the upper eyelids often improves your upper visual field.
Both are valid. Sometimes eyelid surgery including revision surgery is strictly performed for cosmetic reasons. Sometimes the goal is more functional such as when the eyelids are not closing properly, the upper eyelid is droopy (ptotic) or the lower eyelid does not have the proper relationship to the eyeball (turned outward, inward or retracted downward).