If hydrogen bonding in water was weaker, what happens to H+ ion concentration?
The article by Martin Chaplin 'Water's Hydrogen Bond Strength' (arXiv:0706.1355 [cond-mat.soft], no evidence of peer review) is discussing how changes to the properties of water would alter life.  

If the hydrogen bonding in water was stronger, there would be less ionization (less $\ce{H+}$ and less $\ce{OH-}$).

If the hydrogen bonding in water was weaker, there would be more ionization (more $\ce{H+}$ and more $\ce{OH-}$).