In boxing, a fighter can also choose rather than move up to stay at a single weight class and attempt to dominate that weight class. Sometimes, they will even hand select opponents (what tournaments to attend) to pad their record. Due to not always fighting the best, it is entirely possible that these fighters can end with a great record and no titles, sometimes even a horrible record in title fights (world tournaments).
In boxing there is no rules for parity between weight classes. If you fight up, you fight by the weight limits of the higher class.