Austria Under-21 international Weimann curled a 20-yard shot past Stoke keeper Asmir Begovic to give Villa a first-half lead in only his second senior start.
McLeish said: "Goals talk and it will be hard for me to leave Weimann out. It was a fantastic strike. We needed a bit of inspiration at that time and it was inspirational. It came out of nothing and was a wonderful goal from a great young prospect. He is a good finisher and we've seen it again with that goal."
The Villa academy product's stunning strike followed on from his injury-time winner as a substitute against Fulham, although it was not enough to earn his side three points as a trademark Robert Huth header salvaged a draw for Stoke.
McLeish felt Huth's equaliser should not have been allowed or the free-kick leading up to it.
He said: "Jermaine Pennant used his experience to get the free-kick after (Gary) Gardner did not move. Then Robert Huth had two hands on James Collins' shoulders which meant he could not get off the ground to defend the cross from the free-kick."
Stoke were playing their 51st game of the season and earned praise from manager Tony Pulis for their fighting spirit to salvage a share of the spoils.
He said: "That's 51 games we've played now and the second we've had in three days. We lack a lot things but the one thing you can never criticise us for is a lack of effort.
"We were disappointed to be losing. It was a great strike by the kid (Weimann) but someone said it was their first effort on goal.
"I thought we missed some great chances and Huthy, although he's scored a great goal, should have scored off another set play in the first half. To come in 1-0 down at half-time was disappointing."
Source: PA
Source: PA