We present the field and temperature dependence of the magnetizations of BaFe1.9Pt0.1As2 and Ba0.95La0.05Fe1.9Pt0.1As2 samples synthesized by solid-state reaction method.The samples were formed as a single phase in the ThCr2Si2-type structure. Replacing Ba with the smaller La atom results in a lattice shrinkage. The critical current, J(c )(H, T) has been determined (using Bean's critical state model) from magnetic hysteresis loops in a temperature range between T = 5 K and the superconducting transition temperatures (20K), in fields up to H = 9. We find a nonmonotonic 'fishtail' shape (exhibiting a second peak) of the magnetization loops as well as a very large irreversibility. We observe a remarkable flux jump at T = 5 K for BaFe1.9Pt0.1As2 due to magneto-thermal instability, but a very sharp magnetization peak for Ba0.95La0.05Fe1.9Pt0.1As2 near H = 0, which corresponds to a much-reduced relaxation rate of vortices. J(c) decreases exponentially with temperature as well as with field in lower temperatures and fields ranges. La doping causes a considerable increase in the irreversibility, leading to a significant enhancement of J(c) The analysis shows that the high J(c) is mainly due to collective (weak) pinning of vortices by dense microscopic point defects with some contribution from a strong pinning mechanism.