Hoyer threw for three touchdowns on his debut for Rob Chudzinski's side and guided the Browns to their first win of the season against the Minnesota Vikings.
"Don't get hurt," Weeden told the Plain Dealer. "I don't know how else to put it. Injuries suck. They happen. Things happen for a reason and we'll see how it plays out.
"You know, at this point where we're at, that's out of my control. My focus is making sure this thumb continues to make the steps that allow me to get back and be 100 percent."
The Browns are 1-2 going into week four of their season.