We tune optical resonances in rolled-up $\mathrm{SiO}/{\mathrm{SiO}}_2$ microtube cavities by gradually modifying the tube structure through asymmetrical postdeposition of ${\mathrm{SiO}}_2$ . Spectral blueshifts followed by redshifts of the resonant modes are observed in a thin-walled microtube (tube-I), which is attributed to a competition between shape deformation and effective increase of tube wall thickness. In contrast, only a monotonic redshift is detected when asymmetrical deposition is performed on a thick-walled microtube (tube-II). Distinct wavelength-dependent tuning was revealed in both kinds of tubes. Numerical calculations based on perturbation theory are carried out to explain and confirm the experimental results.