Before revision:  We show that if G has treewidth w and maximum degree d, then any MWIS-circuit of G has 2^{\Omega(w/d)} gates and that if G is planar  then any MWIS-circuit of G has 2^{\Omega(w)} gates.
After revision:  We show that if G has treewidth w and maximum degree d, then any MWIS-circuit of G has 2^{\Omega(w/d)} gates and that if G is planar , or more generally H-minor-free for any fixed graph H, then any MWIS-circuit of G has 2^{\Omega(w)} gates.