Williams could make the team if a right-handed first baseman - Andy Phillips or Josh Phelps - does not.
The Yankees already have two right-handers at first base in Andy Phillips and Josh Phelps, with only one expected to make the team.
Weaver worked the eighth inning and allowed four hits, including a three-run homer to Josh Phelps, and a walk.
Josh Phelps is the emergency catcher for the Yankees, who could need to make a roster move.
The original plan was for Mientkiewicz to platoon at first base with Andy Phillips or Josh Phelps.
He was replaced at designated hitter by Josh Phelps, who has essentially lost his spot as the first baseman to Miguel Cairo.
Josh Phelps then hit a two-run single off Steve Karsay, tying the game at 6-6.
Phillips is competing with Josh Phelps, a Rule 5 draft choice with more major league experience, for the backup first-base job.
But he gave up a two-run single to Josh Phelps in the seventh that allowed the Blue Jays to tie the score, 6-6.
Josh Phelps may also contend for playing time at first.