You've got the definitions of weak and strong athesim quite wrong.
Weak atheists do NOT take the position that God does not exist. THey simply do not accept the view that God does exist.
Strong atheists DO accept the position that God does not exist but need not do so dogmatically.
The posiiton you describe as weak atheism is in fact a form of strogn atheism - and it is no less reasonable than the weak atheist position. Arguably more so given that we should assign a low a priori proabibility to the existence of God and the sheer weakness of the case for any particular God existing.