As far as leveling decisions. They were not purposely done to have an edge over any one character as they were done before the fighter was in the party. At the time, the player was playing a bard. I think it was mainly a take that DM multiclass move. I, Unfortunately, roll well during contests. The player who picked the Fighter particularly made his fighter a knight for the Lord the Paladin has committed treason against. So the general character beef is a difference in lawful to chaotic good. Though It also plays into everything else between them. There first interaction was an argument during a council meeting. It was fun to watch.

Intelligence or wisdom to gain leverage on heavy object if they have the materials to do so.

First of all, don't try to restrict your paladin's abilities just because the fighter is jealous. He built his character to be really good at athletics using the expertise feature (he even sacrificed potential paladin levels to get rouge features)! You should let him shine in athletic situations to reward him for his character decisions.

Second of all, it isn't exactly clear what athletics is for, but I also don't use it in brute-force situations. A PC who tries to rip a door off its hinges, lift a heavy object, or break a lock off of a treasure chest generally makes a flat STR check in my campaign. I call for a STR (athletics) check when someone is trying to ford a quickly moving river, climb a steep cliff, throw a rope a long distance, or push a boulder. In the end, it's your judgment call. But when you're on the line, I would lean in favor of offering the character the chance to use a proficiency over not offering it.