do airliners have left and right weight limits as well as fore and aft?
As far as I know the answer is an emphatic "no" ! The distances involved, and the proportions between them just would not allow a significant shift to occur.
Take worst case, ALL passengers on a commercial plane move to one side of the aisle. . . . distance might be ten feet. But lift is still being generated by one hundred feet of wing on each side.
If any professionals know better, I do, of course, stand to be corrected !