However, the 27-year-old believes that despite City being 15th going into the Boro clash, the upcoming fixtures will not determine the fate of manager Stuart Pearce.
"The next 4 or 5 games are important," Weaver told the Sunday Mirror. "When you get on a losing streak and are dragged down into a relegation fight, it can be very hard to pull yourselves out of it."
"When people said we would finish in the top 6 because we beat Arsenal at the start of the season, I didn't listen to them," he added.
"We are a steady Premiership team these days. We are unbeaten in 4 games at home and haven't yet conceded a goal, so it's a bit ridiculous to be saying that the manager is on the verge."