We study the weighted compactness and boundedness properties of Toeplitz operators on the Bergman space with respect to B\'ekoll\`e-Bonami type weights. Let $T_u$ denote the Toeplitz operator on the (unweighted) Bergman space of the unit ball in $\mathbb{C}^n$ with symbol $u \in L^{\infty}$. We give sufficient conditions on $u$ that imply the compactness of $T_u$ on $L^p_{\sigma}$ for $p \in [1,\infty)$ and all weights $\sigma$ in the B\'ekoll\`e-Bonami class $B_p$ and from $L^1_{\sigma}$ to $L_{\sigma}^{1,\infty}$ for all $\sigma \in B_1$. Additionally, using an extrapolation result, we characterize the compact Toeplitz operators on the weighted Bergman space $\mathcal{A}^p_\sigma$ for all $\sigma$ belonging to a nontrivial subclass of $B_p$. Concerning boundedness, we show that $T_u$ extends boundedly on $L^p_{\sigma}$ for $p \in (1,\infty)$ and weights $\sigma$ in a $u$-adapted class of weights containing $B_p$. Finally, we establish an analogous weighted endpoint weak-type $(1,1)$ bound for weights beyond $B_1$. This talk is based on joint work with Cody Stockdale (Clemson University).