In this paper, Riemann-Stieltjes-type integral operators between weighted logarithmic Bloch spaces are considered. Moreover, we give some criteria for lacunary series of new spaces $\mathcal B^\alpha_\omega$ and $\mathcal B^\alpha_{\omega,0}$ which have the weight terms in their definitions. Finally, we prove global Besov-type characterizations for the weighted Bloch space and the little weighted Bloch space.