I've long believed that middleweight isn't a natural weight class. Perhaps one true great middleweight comes along every generation or so who is a natural trained-down 160 pounds for the majority of his career. Hagler, Hopkins, Monzon, Tiger and some other top-tier guys in the division's history were all pretty much true middleweights. Stanley Ketchel seems to also be in this category, although boxrec only has weights on a few of his fights. But other lineal champs of note like Robinson and Leonard and Mickey Walker were all welters who grew into the middleweight division later in their careers. Jake LaMotta fought most of his bouts in the mid-160s, as did Harry Greb, and both Roy Jones Jr. and James Toney were bigger guys who struggled to make middleweight and abandoned the division while still in their physical primes -- so I would argue that this quartet was really a group of all-time super middleweights more than middleweights. And Bob Fitzsimmons was pretty much a light heavyweight if you look at his body of work. Charley Burley was definitely a career middleweight by the standards of his day, but would more likely have been a career junior middle by today's measure. In fact, about half of the top 10 middleweights of all time (depending on your list) really weren't true middleweights -- they were guys on their way up from being prime.
I think you can say the same about most divisions. Look at ww, many fighters who are considered greats there either moved into that division from lower ones or moved up from there to mw.