Every time you have new tyres fitted they rebalance the wheels to suit the new tyres. The old weights are cut off (usually leaving the black sticky residue behind) and then the wheels and tyres are balanced and new weights stuck on in the required place. The fact that there's evidence of old wheel weights on the rim is nothing to signify that they're missing or should be there.
If you have any doubts about the wheel balance, then a good tyre fitters place will balance them for you by removing the existing weights, spinning the wheel up on a machine, and placing new weights where it thinks they should be.
Note: I wouldn't class kwik fit and such like as a place to have them done. They'll bugger it up, try and sell you new tyres, drop your alloy face down and damage it, charge you well over the odds, and probably won't be any
help at all. Find a good local (recommended) place to have them done, but I wouldn't think that vibration under braking is a wheel balance issue, more likely suspension
problem.