Rules for giving away "big item" if you do not have 1000 gold pieces of items to sell
I don't see any reason why either the Charity or the Looting The Body rules should apply here.  (Yes, this situation is somewhat similar to Charity, but it's not the same.)  Just taking the text literally, all it says is:


  [...] you must give them to the lowest-Level player(s) who can carry them!


So that's it.  The only restrictions the rules place on what you can do with your extra Big items are:


You must give them away (if you can; otherwise the next sentence in the rules kicks in, saying you must discard them).
You must give each of them to (one of) the lowest-Level player(s) who can carry it.


Obviously, that does not include yourself, or anyone else who's already at their maximum carrying capacity.  Other than that, since the rules don't say otherwise, you're free to choose among the lowest-Level eligible players.

Of course, if the player you choose to give one of your Big items to is not a Dwarf, they'll probably become ineligible to receive any more Big items, which means that you'll have to offload the rest of your excess Big items onto other players.  (Yes, you may use this tactically: first give your Huge Rock to the Level 1 Thief who just backstabbed you, and then spread your more valuable Big items among players you like more.)  On the other hand, a low-level Dwarf could easily end up collecting all of your suddenly-unwieldy loot, whether you want to give it to them or not.  That's just how things happen in Munchkin.