The Yankees exercised Weaver's $2.5 million club option for 2025 on Friday.
Weaver was saddled with a blown save Wednesday against the Dodgers, letting two inherited runners score while permitting one hit and one walk over 1.1 frames.
Weaver struck out three over 1.2 perfect innings to earn the save in Sunday's 7-4 win over the Athletics.
Yankees manager Aaron Boone said Thursday that while Weaver could close out "a lot" of games, he stopped short of naming the right-hander his closer, Erik Boland of Newsday reports.
Weaver (6-3) picked up the win in an extra-inning battle against the Mariners on Wednesday, allowing one walk over 1.2 scoreless innings while striking out four.
Weaver worked around a walk in a scoreless ninth inning against the Cubs on Friday en route to his first career save. He struck out two batters.
Weaver could be a candidate to receive save chances after Yankees manager Aaron Boone said Wednesday that the team will get "creative" with the closer role going forward, Jack Curry of YES Network reports.
Weaver picked up a hold against the Rockies on Friday, walking one batter and striking out one in a scoreless inning of work.
Weaver picked up a hold with a perfect inning of work against the Orioles on Friday.
Weaver (neck) struck out two over 3.1 scoreless innings Wednesday in the Yankees' 12-0 win over the Pirates in Grapefruit League play. He scattered two hits and one walk.