Water filter kit + iodine tablets (or similar). Extra Nalgene bottles or a big Camelpak.

BRING THE SLEEPING BAG - it's not optional when it gets cold. And it gets cold often, no matter where you are, at night. Same goes for the tent - it's optional if you're staying a weekend, not so much if you're staying for a month. Soaking wet hypothermia is no fun and is bad for an extended length of time.

I might recommend a big hunting knife instead of the multitool but that's up to you. Make sure the knife on your multitool is plenty big. If you do have a multitool I'd make sure it had tweezers. Splinters are hard to remove with only a knife and dirty fingers.

Matches, good hard wood strike-anywhere matches in a WATERPROOF container. Your Bic lighters should also be in a waterproof container.

First aid kit should include antibiotic ointment, an ace bandage, and if desired things like scalpels, tweezers, etc - you can find lists online of recommended camping first aid kit items.

Extra T-shirts - you can rip them up for use as bandages if, God forbid, you injure yourself severely. You'll be glad to always have dry clothes and extra layers, and you can use them to tie things with or as a pillow, etc.

Sandpaper. You'll be surprised when it will come in handy. File your fingernails if you break one, smooth out a whittled end of stick, whatever. It weighs basically nothing and can be useful.

One lightweight pan for cooking food, if desired. Do not bring utensils - you'll be using chopsticks au naturel.

Topo map + a good compass in a waterproof padded pouch. Don't get lost.

I understand the purists among us will scoff at some of these suggestions, but if I were staying a month, I'd want to be comfortable. The point, for me, is to enjoy the woods and get in touch with my survival instincts, not to test my mettle or inconvenience myself beyond reason. Others may feel differently.