Like I said above, I probably wouldn't have even checked if the wallet had any Bitcoin in it, which could've been a waste of my time trying to find a owner of a wallet that has nothing in it.
I see no problem in checking if the wallet has any coins. I would have checked. If it was empty, I wouldn't bother trying to find who it belongs to. And hopefully, the real owner wouldn't deposit any bitcoins on it without realizing it is gone. If it was funded, then I would try to find the owner in a few different ways. You have just left the paper wallet on the beach so that any other person can find it and enjoy this free money or would you have destroyed the paper wallet making the bitcoin supply less by 0.6BTC 
Neither one nor the other. Taking a possibly valuable item (without the intention of using it or profiting from it) isn't the same as stealing it. You are saving it from people who might have other intentions. You are also saving it from water and weather conditions that could destroy it if you just left it there. It's only stealing if you transfer the BTC to yourself or keep quiet about it without doing anything to find who they belong to.