[Paper Kosmonaut]

Heavy large paper? Why heavy? Most models can do with 160 gpm2 or at most 200 gram. And most printers easily can handle that. If you need heavier stuff, print on 100 gram paper and glue that on cardboard.
And as for large, I do have a Brother MFC-J5320DW which also can handle A3 paper (through a slot in the back). But I almost never use it. Lots of models, also the 1/33 ones, are issued on A4 sized paper.
My printer works very well, but once in a while has its occasional hiccup like all printers have. (Mine has a very sensitive paper tray sensor. If I sneeze in my living room, my printer in my hobby room bleeps that 'the tray has gone'. I just need to touch the tray to make the printer realise it still is there.)

I only can say stay away from HP printers They just are plain evil IMHO. Best option when you want to own a printer and want to print a lot is to buy a CISS printer (one where you can refill the ink reservoirs yourself and avoid buying cartridges). I don't yet have a CISS but when I need to buy a new printer I sure will invest in a CISS.
Remember, printers aren't the issue here. Most of them are all right. The issue here is ink. Printer ink is more expensive than blood. Really. Isn't that weird? The printer companies had to find a way to screw us over, I guess... (-: