The way I would look at it is this: All the performance figures of how much runway you are going to chew up in the take off roll, V1 point, obstacle clearance, factoring the thrust setting, are going to be based on the start weight prior to putting the throttles up.
The thing is, that its all worked out for one engine (2 engine plane) from V1, so the reality is in a normal take-off you will exceed obstacle heights anyway, but we can't be 100% certain the engine won't fail can we! But that is a side issue.
If you are overweight at roll start, then you will go beyond the V1 point you should have (on the runway), and now if you were to stop at your overweightV1 you may not be able to before the runway end.
Obviously, this can go further, that if you have really exceeded MTOW, you might not get to VR before the runway end!!!
Think of it this way.
Max Structural Weight when at the gate ready for Push.
MTOW when lined up ready to roll/takeoff.