Did the Marine visit Papua New Guinea during World War 2? Because that's where your piece probably originated from (or from one of the other Pacific Island areas.) I'd guess it was made within the last 150 years or so.
Groups in Papua New Guinea (big island near Australia) still make stone axes and adzes, but basically every rural farmer/hunter used them up until the 1950's or so. I've had a few over the years, they are neat items. Groups there made lots of different styles, pieces like yours, because they are so thin, are probably just decorative examples vs every day tools. The bevel as pointed out is completely wrong for pieces from the US, is completely right for pieces from there. Some are made from a very hard type of greenstone, and that steep bevel is the easiest way to put an edge on it. They use the same technique for making an edge on pieces made from slate/shale and softer stones like yours.
If you are interested in values, let me warn you they aren't that expensive. You'll see some websites where they list them as ancient and sell them for hundreds or even thousands of dollars, but you'll see similar pieces elsewhere for $50. Occasionally you'll see them for sale at auctions or with old papers from the main midwestern authenticators. They started showing up in auctions as WW2 Vets died (80's and 90's), and people assumed they were just really amazing celts found locally where the collector lived. There wasn't a lot of info about them, but they generally sold for very high prices until the internet opened up the world of pictures and information.
Here are some pictures of similar examples, click the picture to see it with more detail. Google Papua New Guinea axe and you'll find pages and pages with the different styles.
Here are some, they are probably oiled up so they look polished. Yours is pretty similar to the middle one, probably similar material, and beveled with that steep bevel.
Here is one from an auction site with handle. I think the handle is actually flipped over. The stone head would go at the top of the picture so the woven part would be the tail of the axe.
A couple more similar to yours.
