It, is fight for the UFC title with less than 10 professional victories, and I really think Weidman at 9-0, will be the last male fighter to fight for a UFC title with that little professional experience.
The fact that so many fighters over the years have fought for the UFC title with so few professional victories is a testament to how new and developing the sport of MMA still is. Many times these fighters were able to crash onto the scene and immediately be the best option available to UFC's match-makers. In Lesnar's case he was easily the most marketable, but had the skill set to push the issue.
I've also seen this used in a debate by a boxing fan, as to why boxing required so much more skill. How could these fighters come in with so few professional fights and fight for, much less win a title? Boxers routinely do not see a title fight until they have twenty or more pro fights under their belts, even after extensive amateur backgrounds.
After Weidman, there are not many fighters on the UFC roster that I could see earning a title shot prior to reaching 10 professional wins. The Women's MMA game is far behind the men's in terms of depth, so I expect that title fights will be contended between relatively inexperienced Mixed Martial Artist on that side of the UFC for at least another 2-3 years.