[MunchkinMan]

Well, Curse! Tiny Hands affects the person it was played on. It says that the victim cannot carry (i.e., have in play) any Item that requires more than one Hand (it says nothing about Big Items whatsoever). Very specifically, the first word describing the effect is "You."

Curse! Cursed Thingy affects an Item, and if the victim has no Items in play, the Curse has nothing to which its effect could be applied. The first two words of the effect text are "One item." Since it doesn't specify who gets to select which Item is Cursed, that means the victim chooses which Item, so long as it meets the criteria described on the card.

Secondly: Neither of these Curses affects Item cards in your hand. Item cards in your hand aren't Items, they're just cards in your hand, and won't be affected by anything that doesn't specifically say they affect your hand.

So, I'll repeat: The difference is in the target. Since you had no Items in play, Curse! Cursed Thingy couldn't affect you because the effect is on one of your Items. However, since Curse! Tiny Hands affects a player, your friend was unable to avoid the effect and would continue to be unable to have multi-Hand Items in play until the Curse was removed.