The Saxons saw plenty of the ball in the Borders during the opening 40 minutes but never generated much in the way of momentum - James Gaskell and Ed Slater sin binned along the way - and paid the price for missing a handful of important tackles.
They had made eight changes to the side that won 23-17 against the O2 Ireland Wolfhounds including a debut for Leicester Tigers lock Slater with Dominic Waldouck (London Wasps) a late replacement for Jonathan Joseph (London Irish) in midfield.
Weir nudged Scotland in front with a fourth minute penalty but after a slow start the Saxons worked their way back into the game only for Hogg's burst down the left to put them on the back foot.
The Glasgow full back's 40 metre run and sidestep under the posts put the hosts 10-0 up after 17 minutes and the Saxons then lost skipper James Gaskell to the sin-bin two minutes before the break for a high tackle.
Weir's second penalty sent them in 13-0 down and the Saxons made an instant change at fly half with Freddie Burns replacing Ryan Lamb and another shortly after with Kearnan Myall taking over from George Robson.
Any route back into the game was halted by Weir's 52nd minute try as he shrugged off two sets of tackles to go under the posts, adding a conversion and a penalty five minutes later with Slater the second Saxon in the sin bin.
Harley forced his way over into the right-hand corner after a close-range scrum and Scott found a huge gap to accelerate through 12 minutes from time.