Construction worker George Glackin, 43, never returned home from work on Tuesday, September 18.
Detectives believe the keen fisherman and walker could have ventured to the Trossachs or further afield.
His brother, Ronnie, made an emotional appeal as police admitted they were growing extremely concerned for the safety of the father-of-five, from East Kilbride.
Mr Glackin's wife Karen Glackin, 49, and stepdaughter Michelle Reid, 19, comforted each other, as Ronnie read out their appeal.
The 47-year-old said: "George, we really miss you and want you to come home. You've done nothing wrong.
"For whatever reason you left, it doesn't matter. Please let us know that you're safe and well.
"Also, anyone else who's seen George in the last couple of weeks, please tell the police."
Mr Glackin, who is partially sighted, had been living with his sister Marie McNamee for the last fortnight before he vanished. Police said Mr Glackin was last seen on CCTV leaving The Spirit pub, in the Saltmarket, last Tuesday.
Chief Inspector Pat Callaghan, said: "George has a number of medical conditions that require daily medication and he hasn't taken that medication with him, as far as we know.
"He's a keen walker and is known to walk considerable distances."
There has been no activity on Mr Glackin's bank account since he disappeared. However, his family believe he has a considerable amount of money with him.