Consider two masses M and m in circular motion with same velocity,v. Both has acceleration v^2/R. The forces acting on the two masses are different. Force will become more on the greater mass. But acceleration of both are same. Because, if you put M and m in the following relation, you get same v^2/R.
since we know $$F/m=a$$
where $$mv^2/R$$ is the centripetal force
also if we want to grant more velocity centripetal force will become more to keep it in circular motion but acceleration expression remains v^2/R with no dependence on mass and increases with increase in velocity.