Weak acids compared to strong ones in pH > 7 solution
When the ratio of conjugate base concenteration to conjugate acid concenteration is more than 1000 , we  say that the  dissociation of acid is complete.
According to Henderson–Hasselbalch equation the ratio of conjugate base concenteration to conjugate acid concenteration gets more than 1000 , when PH-PKa is more than 3.
For strong acids, this ratio is more than 1000 in PH&gt;2 ((  actually it is true for most strong acids )) , but for weak acids , there is no specefic PH . Actually, higher PH , higher dissociation ratio.
So ,when the PH gets higher, the dissiciation ratio gets greater and more poroton will be given up.
Actually, when PH-PKa gets more than 3 for weak acids , they behave like strong acids and allmost all of the acid will dissociate.