What effect do tyre profiles have?

My bike is recommended to run a 120/65 tyre on the front. I know that this means it's 120mm wide and 65% of that high.
If I put a 120/70 on the front, what difference (theoretically) will that have on how the bike handles?
(I had some suspension changes done, and put a 120/70 on yesterday, stupidly - I should've made each change separately. Now I'm chasing handling problems and want to know what part the tyre profile could be playing, hence the question)
If I put a 120/70 on the front, what difference (theoretically) will that have on how the bike handles?
(I had some suspension changes done, and put a 120/70 on yesterday, stupidly - I should've made each change separately. Now I'm chasing handling problems and want to know what part the tyre profile could be playing, hence the question)