First, I feel you numbers are a tad exaggerated.
~At level 6, assuming the target has no AP and no Magic Resist, and Veigar has rank 1 Dark Matter and Primordial Burst, Veigar would need 565AP to deal 1500 damage with just those two spells. If he lands his Baleful strike on you, that is more damage of course, but even basic magic resist runes and base resistances would mitigate that, not to mention 500AP at lvl 6 would be insane.
Also, you got hit by two skillshots, one that is telegraphed and easy to dodge if you didn't get caught out by a stun, and the other that is blocked by two minions, kind of like a Lux stun.
~Assuming the same things, rank 1 Primordial Burst would require 450AP to deal 700 damage. Again, even base magic resists would decrease this a bit. Rank 2, Veigar would need 825AP. That's over 800AP at lvl11. I'm sure it's not impossible, but he'd have to be fed and at that point, you're doomed anyways.
Veigar's skills have great scaling on them. Q has 60% AP scaling, and his W and Ulti both have 1:1 scaling, not to mention the Ulti's addition 80% target AP scaling. This also comes packaged with a great AOE Stun, but Veigar has very real weaknesses.
If you have a dash, keep your distance. Bait out the stun cage and go around or just run. There is a warning and a delay, you have time to avoid it. Don't try to dash out if you get caught inside and focus on dodging the meteor, it's possible. If his team is there, either burn flash to blink over the wall or accept the fact that you got caught out by Veigar. If you get the jump on him, cc him ASAP and burst him before he or his team can respond. Veigar is squishy and, aside from flash and zhonya's is not going to escape your CC or pursuit. If he's ganking you, you need better vision and area control, because his only approach is to either flash in or walk in. If he's a real threat, work some MR into your build. Maw of Malmortis still offers damage, and Banshee's Veil is great for initiators who want to just ignore the wall.
Either you're underestimating how much damage you can really take from Veigar, or you're just not respecting his ability to burst. Veigar is Burst.
