Q.$NH_4OH$ is a weak base because :

The strength of an acid or base is set by how much $H_3O^+$ or $OH^-$ it produces per mole dissolved in water. A strong acid/base is almost completely dissociated; a weak acid/base is only partially dissociated, leaving an equilibrium between the unionised molecule and its ions.

For the general ionisation $HA+H_2O \rightleftharpoons H_3O^++A^-$, the equilibrium constant is $K=\dfrac{[H_3O^+][A^-]}{[HA][H_2O]}$. Since water is present in large excess and its concentration is essentially unchanged, it is absorbed into a new constant, the acid dissociation constant $K_a=\dfrac{[H_3O^+][A^-]}{[HA]}$, which directly measures acid strength -- a larger $K_a$ means a stronger acid. Strong acids such as $HCl$ have very high $K_a$ (e.g. $\approx2\times10^6$ for $HCl$ at $25^\circ C$); weak acids such as formic acid ($K_a=1.8\times10^{-4}$) and acetic acid ($K_a=1.8\times10^{-5}$) are only partially ionised. As a rule of thumb, an acid with $K_a>10$ is considered strong and one with $K_a<1$ is considered weak. …