And while defeats to Wales and France on the last two weekends of action wasn't what Weir and co were looking for, the Glasgow fly-half insists the side have made major strides given that they ended last year's tournament with five losses and the Wooden Spoon.
"We feel we had a wee bit more to play for this year, especially with how close this championship was. If we had won against Wales, we'd have gone to Paris in a really good place and possibly in contention for the title," Weir told the Evening Times.
"It's disappointing that didn't turn out but having finished sixth last year with five defeats, what we have done this year is a great step towards going on and pushing for the Championship next year.
"We've always had that squad spirit and desire to give 110%. The results just came down to some small areas - the bounce of the ball or the accuracy of us kicking from our own half.
"Those things haven't always matched our effort levels. But once that works out, I'm sure this team will go all the way to the top and cement ourselves as title contenders every year."
Scotland were beaten 23-16 by the French in Paris on Saturday night but were well in the hunt for a famous victory for much of a hard-fought encounter at the Stade de France.
Scotland led 6-0 at the break and were still on level terms at 9-9 until a converted try from Wesley Fofana swung the game in France's favour with 15 minutes remaining.
"It was tough to take because after 60 minutes the crowd were almost about to turn against the French," added Weir, who made his second Test start having being picked ahead of clubmate Ruaridh Jackson for the game against Wales.
"We felt we could go and sneak it at the end. But after they scored their try they got a bit of momentum and pushed on.
"It was hard with the conditions. Especially the first half when the rain was coming down heavy and the surface was greasy underfoot.
"It wasn't perfect but the rugby we did play in the first half was great - up there with the best of our Championship. It was just a shame we couldn't do that in the second half."