Most airport restaurants will pack up meals to go, even the nicer ones. I often get food to take on planes since I don't want to pay $6 for a snack box on my flight. You might be able to find a nice deli sandwich or entree-sized salad. If you really need to check luggage and are worried about picking it up, I'd get a meal to go from one of the restaurants in the secured area, pick up my bags then find a place where you can sit comfortably and eat while you wait.

That said, I'd try to do carry-on only as well. You'd be surprised how little you need for a week long trip. A 3-4 oz. saline should be plenty, and Oakleaf makes a great point about medical liquids. If you have a Rx lotion I imagine that would qualify too.

For non-Rx stuff I try to use what's available in my motel/hotel or borrow from my hosts (If I don't know them well enough to be borrowing toiletries, I'm not staying with them!). It might not be what I would ordinarily choose to use, but it gets the job done. I'll make an exception if my skin/scalp is acting up, then I'll bring my own shampoo/conditioner using humangear Go Toob bottles. They don't leak and they don't explode. there's also a ring in the cap that you can rotate to indicate the contents. And they come in several sizes, but I find I can stretch 2oz. over a week if I alternate it with what's locally available.