Answer is: because weak acids do not dissociate completely.
The strength of an Arrhenius acid determines percentage of ionization of acid and the number of H⁺ ions formed.
Strong acids completely ionize in water and give large amount ofhydrogen ions (H⁺), so we use only one arrow, because reaction goes in one direction and there no molecules of acid in solution.
For example hydrochloric acid: HCl(aq) → H⁺(aq) + Cl⁻(aq).
Weak acid partially ionize in water and give only a few hydrogen ions (H⁺), in the solution there molecules of acid and ions.
For example cyanide acid: HCN(aq) ⇄ H⁺(aq) + CN⁻(aq).