How? From top-down photos the J-20 is almost just as large as a Flanker.
As for weight I believe EMALS catapult solve the weight issue.
Personally I agree with the thought that J-20 is ready, more proven, more capable than J-35/xy because it has to be... it's larger and can accommodate more things, powered by more powerful engines. These should translate to electronic advantages not to mention better range and payload which are certainly important for any fighter. The issue is we don't have all the information from which these decision are based on. It could have been in the "wisdom" of the decision makers that on the grand scheme of things, an inferior fighter from SAC is more suitable for PLANAF simply because SAC should have the work. It could be nothing more than that (but I doubt).
The general conclusion based on this is that the J-35/xy is more suited to the carrier role because the advantage of being able to squeeze more fighters in 00x carrier more than compensates for any would be loss of capability if a J-20 navy variant was developed. All of this stuff
should have been carefully calculated and likely conflict scenarios and SWOT assessment being considered. As a more regional defensive role, a smaller fighter may have been considered acceptable so that an extra one or two fighters could fit on the 003 and who knows what the plan is for 004 and onwards. They would have thought J-xy and Type 004 when making the decisions.
As for J-20 being flanker sized, well it's still larger than the J-35/xy and while the wingspan is similar, it's much longer and surely heavier.