We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields{,} we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer{,} and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear{,} envisioning the engineering of rheological devices at the microscales.