McMahon has been plagued by injuries in recent months, the most recent being a sprained ankle sustained during pre-season, but narrowly missed out on a place in last weekend's squad that faced Brentford.
However, Weir admitted he hoped to avoid curtailing his progress but could use him sparingly in the coming weeks.
"Tony, through no fault of his own, has been 'stop start' pretty much all of the summer," he told the Sheffield Telegraph.
"So, with that in mind, we wanted to make sure that he had a good fortnight's worth of training under his belt before coming back.
"Otherwise, there's a danger he might have to repeat the process and go through the same thing all over again. That wouldn't serve a purpose for anyone whatsoever."
- Sports & Recreation