
I have got 7J x 15" 'Team Dynamic' 12 spoke wheels on my Velocity. They are presently fitted with 195-50-15 tyres.
I would like to go wider on the rear...say 205's or 225's
What can I go for on these rims and whats it likely to do to handling etc? 

I fitted 225 R888's rear tyres on a 7" rim with no problem when I had my zx10r turbo Indy,it felt ok,but when I removed the turbo,and just ran the stock zx10r engine I went down to 205's,and it felt alot better on those,I just had 195 50 15 on the fronts.
You might find this fitment guide useful.
Having posted that I have a set of 225/45 R888s on 16/7j rims and they get used for track days on a 1100Kg car with no issue. Except for needing
35psi or more to keep the wear mark off the side wall!