Complex sentence: Griffin's debut performance was further rewarded after he was named "NFL Rookie of the Week", and he was given that honor once again after the Redskins' win over the Tampa Bay Buccaneers in Week 4.
Split into simpler sentences: Griffin's debut performance was further rewarded after he was named NFL Rookie of the Week. He was named Rookie of the Week for the second time after the Redskins' win over the Tampa Bay Buccaneers in Week 4.