There are two different versions of Wesker to unlock for the mercenaries mode in Resident Evil 5.
The first is Midnight Wesker, which is unlockable by getting an A rank on The Mines in mercenaries mode.
The other outfit, STARS Wesker, is unlocked by getting an A rank in The Prison in mercenaries mode.
Getting an A rank requires either 40,000+ points in single player mode, or 80,000+ in either co-op mode.
If you’re looking for some help for the mercenaries mode, check out my mercenaries mode strategy guide.