The NFL considers Meriweather a repeat offender, and he was flagged twice in the Redskins 45-41 victory over the Chicago Bears on Sunday.
He will miss this weekend's game against the Denver Broncos and a Nov. 3 contest against the San Diego Chargers.
Meriweather was fined $50,000 for multiple hits on Baltimore Ravens tight end Todd Heap during a 2010 game, then was fined another $45,000 in fines in 2011.
"I feel like every hit that I took was a legit hit," Meriweather said, via the Washington Post. "I wasn't trying to be dirty. I wasn't trying to hurt nobody. I didn't launch with my head. I used my shoulder like they told me to do. Everything I did was a pointer from them (league officials). ... You've just got to play. There ain't nothing I can do about it. I just go out there and play."Earlier this season, he got tagged with a $42,000 fine for knocking out Packers running back Eddie Lacy with a helmet-to-helmet hit.