Why does baseball start during the week and play day games but then go to night games and weekends?

Actually, there aren't many mid-week day games unless there's a double-header. That said, there are a few games each season that are mid-day mid-week games, because it's fun to play hookey for a day from work and go to a ball game.
Day games in general are becoming increasingly rare, however because to the TV networks who would rather maximize their advertising revenue by having the games they televise occur during prime-time. The majority of day games are played on Sunday nowadays.