pre 16 minutes, veigar is significantly weaker than nearly all other ap mid laners. mid game he breaks even in damage with other mid laners however hes dependent on his team mates to get anything done whatsoever, veigar cant afford to get caught at all or else hes just dead meat. beyond 35+minutes veigar is stronger than nearly all other ap mid laners and can just stay outside the fight and Q harass and his team will win the fight the longer it goes on, or veigar will R+Q a carry and it will result in a kill. beyond 45+ minutes veigar is a god in terms of damage dealing no matter what.
at no point in the game can veigar play make, he can only punish out of position players or people who make mistakes, veigar cant 1v1 or handle poke/dives.
he is dependant on his team to accomplish anything.
this assumes 100120 farm at 16mins with at least 70+ bonus AP farmed (i generally have 90110)
at 35mins its about 220~250bonus AP with around 250 farm.
beyond 40+minutes its whatever i can get away with in lane without my team getting destroyed or getting cheesed flash ulted, you name it. i can get up to 400~500AP pending how long the hour long game drags on for.
veigar is the definition of late game scaling, he has infinite potential, he just needs a team to back him up or captialize on veigars strengths, if you have a team with a good front line, sejuani/nautilus/renekton/ whatever adc, and veigar, thats fantastic, they can keep veigar alive and give him ample opportunity to land meteor and R who he pleases.
but if you have a team like rengar who is going to dive the back line, xinzhao who is going to attack the first thing he sees, morgana support, and whatever adc, you wont have any immediate peel for the veigar (morg binding could miss, or it could just be too late), with such a team veigar will often get poked/focused and he will just die before he gets anything done.