Heavy controller? You sure they didn't weigh it down a bit so it wouldn't get flogged? The Gamepad is quiet light for it's size and for it's components. It's actually not much heavier than an XBOX controller.
It does feel weird at first coz other controllers are smaller and more comapct. And as for long gaming sessions, it's not like you hold it up towards the screen, you just rest it in your hands or lap like you do when using PS3 or XBOX controllers.
As for the screen, depending on the game, it can either be used partly in game as an in-game menu/pasue menu, map, and some games have off-screen play, which means you can play the game on the Gamepad screen alone. This is good if the wife or kids want to use the TV, or you want to play in bed or elsewhere in the house. I also installed Netflix on my Wii U so i can watch TV show and movies on my Gamepad. Great stuff.