Chickens can certainly get too fat, and yes, they will sit as if hatching eggs when they are truly broody, even if there are no eggs. But unless she stays on the nest literally all the time, except once a day for a few minutes to take care of business, she is not yet truly broody, and maybe not...
Maybe nothing. Broodiness is a possibility, but she should stop laying very soon if not now, if she is. Normally. once they lay their clutch of a handful of eggs, they stop laying and stay on their chosen nest 24/7, except for one outing a day. She could be headed in that direction. I...