Weak acids compared to strong ones in pH > 7 solution In the book of Molecular Cell Biology (Big Alberts) by Alberts, at page 46, it is stated that

Acids—especially weak acids—will give up their protons more readily if the concentration of &gt; H3O+ in solution is low and will tend to receive them back if the concentration in solution is high.

Does this mean that, in a solution with high pH, the weaker acids will behave like a strong acids in water, in the sense that they will be more inclided to give up their protons compared to strong acids?
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.