Well, these are just my thoughts, hopefully someone who plays Veigar (because I don't) can give some valid counter-tips.
But from my experience of playing against veigar, if his "Event Horizon" (circle stun thing) is becoming too much of a problem, you may want to consider buying Mercury's Threads, especially if their team is "cc-heavy".
Apart from that, you have to remember that his stun only works if you run into the edges of his "Event Horizon". I've seen players who automatically panic/ or arn't paying attention when Veigar casts his "Event Horizon", and end up getting caught in his stun. Try to run around within the edges of the "Event Horizon" while dodging most of his skill shots, and wait out the Event Horizon that way.
Also, this is something I've observed with some Veigar players. After they cast "Event Horizon", some players tend to move forwards, which can put them in range of your auto-attacks/abilities. So, if you can manage to not get caught by the stun, and instead run around inside it, maybe you can end up trading attackes, or even coming out ahead in the trade. Either way it's better than getting caught by the stun and receiving Veigar's full combo. :/
I hope this helps.