I wrote "Many college students work at the weekends." My colleague changed 'at' to 'during' = Many college students work during the weekends. Do you feel there is a difference, however subtle?
Yes, there is a significant difference.
Works at is usually used for a place (He works at the telephone company) or solving a particular problem (He's working away at it now).
Working on (3.a.) is used for times (he works on Mondays through Fridays; he also works on weekends sometimes) and problems (He's working on it now).
During is acceptable, as is They work weekends.