Are priests limited to saying only three Masses during the weekend?
Priest are limited in how many Masses they may say, as canon law states:
Can. 905 §1. A priest is not permitted to celebrate the Eucharist more than once a day except in cases where the law permits him to celebrate or concelebrate more than once on the same day.
§2. If there is a shortage of priests, the local ordinary can allow priests to celebrate twice a day for a just cause, or if pastoral necessity requires it, even three times on Sundays and holy days of obligation.
In the USA most Bishops grant their pastors and priests to celebrate twice on a weekday and up to three times on Sundays and holy days of obligation. So the limit is not based per weekend but per either weekday or Sunday. If a priest were to exceed his limit in violation of the canon then his celebration of the Mass is illicit but still valid and all who attend still fulfill their obligation.