We study the weak interaction axial form factors of the octet baryons, within the covariant spectator quark model, focusing on the dependence of four-momentum transfer squared, Q 2 . In our model the axial form factors GA(Q 2 ) (axial-vector form factor) and GP (Q 2 ) (induced pseudoscalar form factor), are calculated based on the constituent quark axial form factors and the octet baryon wave functions. The quark axial current is parametrized by the two constituent quark form factors, the axial-vector form factor g q A (Q 2 ), and the induced pseudoscalar form factor g q P (Q 2 ). The baryon wave functions are composed of a dominant S-state and a P -state mixture for the relative angular momentum of the quarks. First, we study in detail the nucleon case. We assume that the quark axial-vector form factor g q A (Q 2 ) has the same function form as that of the quark electromagnetic isovector form factor. The remaining parameters of the model, the P -state mixture and the Q 2 -dependence of g q P (Q 2 ), are determined by a fit to the nucleon axial form factor data obtained by lattice QCD simulations with large pion masses. In this lattice QCD regime the meson cloud effects are small, and the physics associated with the valence quarks can be better calibrated. Once the valence quark model is calibrated, we extend the model to the physical regime, and use the low Q 2 experimental data to estimate the meson cloud contributions for GA(Q 2 ) and GP (Q 2 ). Using the calibrated quark axial form factors, and the generalization of the nucleon wave function for the other octet baryon members, we make predictions for all the possible weak interaction axial form factors GA(Q 2 ) and GP (Q 2 ) of the octet baryons. The results are compared with the corresponding experimental data for GA(0), and with the estimates of baryon-meson models based on SU (6) symmetry.