Matter-free lattice gauge theories (LGTs) provide an ideal setting to understand confinement to deconfinement transitions at finite temperatures, which is typically due to the spontaneous breakdown (at large temperatures) of the center symmetry associated with the gauge group. Close to the transition, the relevant degrees of freedom (Polyakov loop) transform under these center symmetries, and the effective theory depends on only the Polyakov loop and its fluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified numerically, for the U(1) LGT in (2+1) dimensions, the transition is in the 2D XY universality class, while for the Z_{2} LGT, it is in the 2D Ising universality class. We extend this classic scenario by adding higher charged matter fields and show that the critical exponents γ and ν can change continuously as a coupling is varied, while their ratio is fixed to the 2D Ising value. While such weak universality is well known for spin models, we demonstrate this for LGTs for the first time. Using an efficient cluster algorithm, we show that the finite temperature phase transition of the U(1) quantum link LGT in the spin S=1/2 representation is in the 2D XY universality class, as expected. On the addition of Q=±2e charges distributed thermally, we demonstrate the occurrence of weak universality.