Austrian Weimann scored just before half-time, then N'Zogbia, once thought to be part of Paul Lambert's 'Bomb Squad', doubled Villa's lead.
Villa boss Paul Lambert said: "One of the big factors in their favour was the heat. We're certainly not used to that - the conditions were really, really tough.
"I have never experienced heat like this. It is really tough, even when you're walking around. It's pretty exhausting at times.
"But I was delighted with the two teams I put out. I thought we dominated the second half. But it was a hard, hard game overall.
"The first half was tough because the heat was greater in that period. But the lads were resolute. "We were strong defensively and never really got hurt.
"Andi scored a very good goal. Darren did great for it. The goalkeeper might have saved it - should have saved it.
"But I said to Andi afterwards that it doesn't matter how they go in, it's about them going in.
"The second was a top-class finish. I thought the goal from Charles was first-class. It was a well-taken goal."
For the big stories and the banter follow us on Twitter: @tribalfootball