Good advice from vintage! Another tip would be to just hold on to the bridge as you turn the pegs. To get leverage, put the violin between your legs otherwise it is hard to get enough push into the peg box to make the pegs stick. By having the violin between your legs and holding the bridge, you should be able to have more confidence tightening without worrying about the bridge collapsing. You could also have a bridge issue as Vintage is saying. Make sure the wood of the bridge is unbent, otherwise you may need to get a new bridge. Most the time though it is just a matter of holding the bridge while tuning the pegs.