  We give sufficient conditions for finiteness of linear and quadratic refined
Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing
depth $\leq 2$ quotients of the fundamental group, following a construction of
Balakrishnan-Dogra in the projective case. We also apply Betts' machinery of
weight filtrations to give unconditional explicit upper bounds on the number of
S-integral points when our conditions are satisfied.
