I have a litter of two, nearly 5 weeks old. They were born by C section, and other than feeding and cleaning them, mum has never wanted to spend time with them in the whelping box. They are fit and healthy, thriving, but now scream to be picked up and cuddled/given attention. Their playpen is in the living room, so they are always a part of family life. I don't want them to become spoiled brats who are overly demanding, but they are a toy breed that was bred to be a companion, so I understand their need for human company. Are they insecure because mum wasn't overly attentive? 
She does play with them now they are bigger, she just isn't keen on snuggling with them. Should I pick them up when they cry? I have never known puppies so young be so demanding.

I've never had pups screaming.  Have they been vet checked.

Ours certainly do, they sound like demented Seagulls, and it is often for attention rather than being hungry or needing to be clean, though the latter is something my breed will do by 4 weeks as they hate to be dirty near where they sleep.

They are definitely not ill, they just want picking up lol. They start with squeaking, then it escalates to screaming if I ignore them, which stops instantly if I pick them up. They do play together happily in their playpen, but when they want a cuddle they shout the house down!
They are both able to exit the box and are happily using the pads for toileting, they just want a lot of attention. I just worry that by responding to their demands I am creating monsters who will expect me at their beck and call. I wouldn't pick up an older puppy who was so vocally demanding, but they are so young, it is hard to hear them cry.

Had this with our giant breed from about 4 weeks old - I have a video of them screaming in Facebook !

If they are not quite 5 weeks yet, and mum isn't spending time with them, they must be feeling dreadfully lonely as you have a breed that must stay with their mums for at least 12 weeks. If mum won't do it, you will have to take over. Or don't they stop if you let them out of the pen? Like Brainless I also refer to demented seagulls as that's what puppies sound like, but it always stop when they get to run around and aren't confined. And at that age it doesn't take a lot for a toy breed to get tired out and they can then go back into the pen.

They stop the second I pick them up. They have lots of room to play in the pen, they just want to be cuddled. I have been trying to preempt the screaming by getting them out as soon as they wake up, and it seems to be working. I am happy to give them as much attention as they want, (who needs an excuse to cuddle baby puppies?!) I just worried I was encouraging demanding behaviour.
Best of all, mum chose to sleep with them last night. She seems to like them a lot more now they are proper tiny dogs, spends a lot of time playing with them, which is great. This is my first litter by C section, I am really shocked at how much it seems to alter the bitch's behaviour towards her pups. This girl had a litter before she came to me, no C section required, and was a brilliant mum according to her breeder.

I had that with a singleton pup.  Luckily mum was wonderfully patient and would stay with her most of the time - even at 6 and 7 weeks, but if mum or me left the little brat alone for more than a minute the screaming started. 

I suppose only having 2 puppies, they rely on human companionship because they haven't got lots of litter mates.  There really is nothing you can do.  Picking them up shuts them up, so you will always do it.  I did!!

Mine all start this malarkey around 5-6 weeks!
It brings the house down and I'm always afraid they wake the whole district. My poor husband often gets up before me and has to face this so have devised a plan.
He creeps into the kitchen with a handful of kibble in his hand ( kept strategically by the door) which he broadcasts all over the floor.
They career around finding the bits while he gets their proper breakfast ready.
He puts that down just as the 'hide and seek' is done. Blissful quietness.

You won't be creating monsters...just human centred companions.