Athletic Supporters
Although there is no evidence that athletic supporters prevent hernia (which, contrary to popular belief, are rare among lifters) or any other injury, many male weightlifters feel more comfortable wearing them or some kind of brief that offers support.

Briefs Under Lifting Suits
Most men and women wear some kind of brief under their lifting suit. Such a brief is handy during the weigh-in, makes most athletes feel more comfortable and, in the unlikely event of a shift in the suit or a split seam during a lift, the brief will serve to maintain a level of privacy for the lifter.
In addition, wearing a support brief will make it more comfortable to pull the bar close to the body.

Shorts & Competition Rules
Some athletes wear shorts over their lifting suit in competition and/or sweatpants in training. This is permissible in competition as long as the shorts fit the body closely (baggy gym or boxer shorts are not permitted).
Some referees interpret the rules as requiring that the shorts be worn under the uniform. The nature and purposes of bicycle shorts has already been discussed.