The young forward kicked five goals in the opening half of the Bulldogs' win over the Giants but dislocated his elbow in the third term. Weightman played out the match and trained on Wednesday after avoiding any bone damage, but Beveridge indicated that the club would err on the side of caution heading towards the end of the season.
"It's a pretty traumatic sort of injury, and he is going to train today but we want to make sure that if he if he plays, he's pain-free, he's comfortable and he can play his natural game," Beveridge told media.
"Standing in front of you, I'm not totally certain that that will be the case.
"He'll definitely train and I think we're more inclined to look after him and he'll need to miss a game. But I'd say he'd almost definitely be ready for the following week."
The Bulldogs are also unlikely to welcome back Josh Bruce as he continues to make his comeback from an ACL injury. The 30-year-old played in the VFL last week and looks set for another run in the seconds as he continues to regain match fitness.
Tim English has already been confirmed as an out after entering concussion protocols, while Beveridge remained tightlipped on where Lachie Hunter, who featured for Footscray alongside Bruce on Friday night, will be playing this weekend.
Sitting one game outside the eight as we approach Round 15, the Bulldogs have a difficult run home to secure a finals spot. With games against Hawthorn, Brisbane and Sydney in the coming weeks, Beveridge is hesitant in looking too far ahead.
"Beyond this game we've got a stretch of playing against teams who are above us, which is a fact," he said.
"But Adelaide beat us by a point. There's been other teams everyone was expecting us to beat but you're either good enough or you ain't.
"We believe our best is going to challenge but as we discussed this morning the momentum swings in games we've got to stave off and we're setting ourselves up each week to be a formidable opponent."
The Bulldogs and Hawks are set for kickoff at 7pm (AEST) on Friday night at Marvel Stadium.