We obtain certain sufficient conditions under which the couple of weighted Hardy spaces $$ \left({H}_r\left({w}_1\left(\cdot, \cdot \right)\right),{H}_s\left({w}_2\left(\cdot, \cdot \right)\right)\right) $$ on the two-dimensional torus đ2 is K-closed in the couple (Lr(w1( · , · )), Ls(w2( · , · ))). For 0 < r < s < 1, the condition w1, w2 â Aâ suffices (Aâ is the Muckenhoupt condition over rectangles). For 0 < r < 1 < s < â, it suffices that w1 â Aâ and w2 â As. For 1 < r < s = â, we assume that the weights are of the form wi(z1, z2) = ai(z1)ui(z1, z2)bi(z2), and then the following conditions suffice: u1 â Ap, u2 â A1, $$ {u}_2^p{u}_1\in {\mathrm{A}}_{\infty } $$ , and log ai, log bi â BMO. The last statement generalizes the previously known result for the case of ui ⥠1, i = 1, 2. Finally, for r = 1, s = â, the conditions w1, w2 â A1 and w1w2 â Aâ suffice.