Defoe, 36, and Davis, 34, both joined on loan in January but have yet to make a significant impact. The hefty wage outlay on the pair is now coming under scrutiny in the wake of the Scottish Cup loss to Aberdeen on Tuesday.
The 2-0 home defeat will condemn Gerrard to a trophy-less first season as Ibrox manager unless he can somehow bridge the eight-point gap with Celtic at the top of the Premiership.
Weir was 36 when he arrived at Ibrox in January 2007 as a six-month stop-gap, but went on to become captain and accumulate eight trophies before leaving five years later.
He did so by coping with the ageism that Defoe and Davis must face down now.
“I think when you are at the stage they are, it is like Rangers in the title race,” he said. “When you have a bad game, or lose a couple, people say you are out of the title race.
“It is the same as a senior player. When you are 36, 37, 38, 39 after one or two bad games, people will be writing you off so you know you have to be on it every single game.
“You can’t take shortcuts, you can’t skip steps, you have to be the best prepared you can be and fully concentrated on the pitch because you know if you have a bad game or make a mistake it is the end of your career; the end of the world in some people’s eyes. When you are 23 that isn’t the case. You have to be focused, realise there is going to be an increased level of criticism and a lot more conclusions from it.
“As you get older I definitely think you feel the pressure more. Especially in Glasgow [and] with Celtic pushing for ten-in-a-row, eight-in-a-row, or whatever. It comes with it, that pressure.
“If you are younger you go and enjoy it and go and play and don’t have the baggage you do have when you are older and have been through bad times and know what it is like not to win a league or have the opposition being successful.
“You have to be mentally strong. That goes with the territory playing for Rangers or Celtic. No matter how good a player you are, if you can’t deal with that then it becomes a real struggle and it can weigh you down. We’ve all seen loads of players who have come up here and we know are really talented and have done well in other leagues but the actual intensity and scrutiny and pressure you are under, can put some players under.
“It is something you either adjust to, or get used to. I would never say you actually get to the stage you actually like it, you just see it as the terrain and you survive it.”