Harry Maguire struck the winner after substitute Enoch Showunmi cancelled out Kevin McDonald's first-half opener. County were reduced to 10 men in the 14th minute when Gary Liddle was red-carded for a reckless challenge on McDonald.
Weir said: "It's enjoyable to start with three points. I thought we played well and obviously the sending off changed things.
"I think we learned a lot of things. There were a few questions asked of us and we came through it well.
"We were one-nil up and they were down to 10 men, which adds a bit of pressure. It's a difficult thing for players to deal with and I thought we handled it really well.
"We were patient and we kept passing it and moving. We kept creating opportunities and doing the right things. There are always things you can improve on and that's the environment we're trying to create here."
Notts County manager Chris Kiwomya expressed his disappointment after seeing his side come from behind to level.
He said: "I'm disappointed because I thought we got back in the game and rode our luck, which you have to do with 10 men.
"For the sending off, his foot was high but he did get the ball. I don't know if the referee was in a great position to see it. I was disappointed with some of the referee's decisions. You need some things to go for you.
"I can't ask for more from the team as a working unit. We got back in the game with ten men and that tells you a lot.
"We were looking at making different changes. I said to the lads at half-time that it would be the changes that made the difference. Enoch came on and took a great goal.
"The new players worked hard and did very well. It's a bit deceiving when you're playing with ten men because the players have to cover more ground.
"There are good teams in the division and I think after seven or eight games you'll have a better pattern. I'm very happy with my squad."
Kiwomya confirmed that County are close to signing Celtic's Australian midfielder Jackson Irvine on loan, adding: "Hopefully that will get done and he'll be available for Wednesday."