Is there a standard set of rules, or do they vary from tournament to tournament?

I'm more interested if there is a universal (or common) set of weight categories. If anyone knows that'd be great.

There are generally established rules for all tournaments, as well as weight classes. However, the rules and weight classes can vary, depending on the tournament. And like MMA, after the weigh-in, most participants put some weight back on before the fights. A reputable tournament will publish the rules and weight classes ahead of time. It's different than Judo tournaments where often times you weigh in as you arive and fight at that weight.

This is a link to the IBJJF site's rules:

http://www.ibjjf.org/rules.htm

no eye gouging