Here is my understanding of player weights:
Each owner has their own techniques or game they like to play. By editing the default weights, it lets you pick and choose as to which attributes you would want or prefer for your team. For example, lets say you value a running back that has really good catching skills. When you go to edit player weights, you set the value for pass catching and route running higher than other attributes. This raises the default (or lowers if this is a bad attribute) rating for those with good catch and route running to a higher number, therefore this player would now have a higher rating (for you) for your style of play.
The player will not perform better because you edited their weights, it simply acts as a filter for those players and the specific attributes you want to collect on your team.
Hope this helps!