not to be captain obvious, but in general, i'm assuming that fairway width is closely tied to length of the hole. the age of the course and the quality and type of course also factor in.
longer holes tend to be designed with wider fairways to accommodate use of the driver, while shorter ones might promote use of a long-iron or fairway wood
older public courses will generally have wide fairways even on short to mid length par 4's because they likely weren't considered 'short' when it was designed, unless the course has been updated and lengthened (or tightened).
most private courses (not that I've played any) seem like they're designed to challenge members, who are likely avid golfers, with narrow fairways and numerous hazards, while some resort courses in vacation getaway spots seem to have a lot of wide open fairways to promote a more relaxed, stress-free 'fun' round of golf.