Smith took Weir to Everton in 1999 and called on his services again as Scotland manager before luring the 37-year-old to Ibrox in January.
"I have to say he is the best pound-for-pound signing I've made," said Smith. "He has done it on three occasions for me as you have to look at what he did when he came back for Scotland."
Smith believes Weir has been a shining example to his team-mates both on and off the park since his arrival at Rangers.
"I think Davie is good for any young player and even the guys in their late 20s, who want to play for as long as possible," he said.
"Any player who plays to that age has to sacrifice something and he dedicates himself to his profession. I would hope a lot of the other players look at him and try to pick up good habits from him.
"At Everton, it was a natural thing for them to look at him and think 'how long can he go on?'
"But, when I see the way he is playing for us, he is beating that argument by making us aware that he brings something to the team that few people can do.
"I don't know how he keeps going, but he doesn't like to take his days off.
"He does things properly, makes sure he gets plenty of rest and it seems to work for him.
"He has been terrific lately, not just for Rangers but for the international team as well.
"I said to him during pre-season training that maybe he shouldn't do as much as the rest of them, but he did every bit.
"He doesn't like to be looked upon as being different from anybody else and it has stood him in good stead.
"I think he is looking at a lot of players across Europe at the moment who are playing into their late 30s and sometimes 40s. He's only 37 so he's thinking he can keep going."