"It's a moment I'll cherish and hopefully I can do the coaches justice for giving me the start," Weir said of his selection for the penultimate match in the 2013 edition of the competition.
Euan Murray is restored to coach Scott Johnston's selection, having missed the 12-8 win over Ireland for religious reasons. Geoff Cross, who replaced him at tighthead, drops to the bench.
Scotland interim head coach Scott Johnson said: "Selection is tough just now but that's a good thing as we increase competition for places.
"Duncan did well when he came on against Ireland and he got some decent game time for Glasgow at the weekend. He's a talent with a really good work ethic and a thirst to improve, which I like a lot.
"Ruaridh remains a key part of our squad but he knows with Tom Heathcote proving a match-winner for Bath and kicking goals from here, there and everywhere, that he needs to up his game too.
"Geoff Cross was a standout against Ireland and it's up to Euan, who fronted up big time against Italy, to raise the bar again.
"Wales will be going for their fifth successive away victory in the championship and that would be a record for them but our focus is on ensuring we win the contact zone, continue to improve and make it three wins on the bounce."
Scotland: 15 Stuart Hogg, 14 Sean Maitland, 13 Sean Lamont, 12 Matt Scott, 11 Tim Visser, 10 Duncan Weir, 9 Greig Laidlaw; 1 Ryan Grant, 2 Ross Ford, 3 Euan Murray, 4 Richie Gray, 5 Jim Hamilton, 6 Robert Harley, 7 Kelly Brown, 8 Johnnie Beattie.
Replacements: 16 Dougie Hall, 17 Moray Low, 18 Geoff Cross, 19 Alastair Kellock, 20 Ryan Wilson, 21 Henry Pyrgos, 22 Ruaridh Jackson, 23 Max Evans.