The paper can be understood as a completion of the $q$-Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear $q$-difference equations. The $q$-Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice $q^{{\mathbb{N}}_0}:=\{q^k:k\in {\mathbb{N}}_0\}$ with $q>1$. In addition to recalling the existing concepts of $q$-regular variation and $q$-rapid variation we introduce $q$-regularly bounded functions and prove many related properties. The $q$-Karamata theory is then...