Some synthetic stocks have a hollow cavity in the buttstock behind the recoil pad into which you could insert one of the mercury recoil reducers (most of which weigh between 1/2 to 1lb.) marketed for shotguns. Or you could fill it with your desired amount of lead shot and then fill the empty space with some of that expanding foam spray insulation. I've also seen synth stocks that have hollow space in the fore end which could also be filled with lead shot and epoxy. Why do you want to add weight?

Mike