@optimisticpessimist has given you some great information about how things work with the extra money he would get for having dependents. The military would consider him to be your sponsor. He would be responsible for you and if you did anything to get in trouble (even something as simple as a speeding ticket on post), his command would be notified about it and he could get in trouble. As @optimisticpessimist pointed out, the only thing you would get from the military, is the health insurance and that’s only once he adds you to DEERS. If you guys wanted dental coverage, he’d have to pay for it out of his paycheck. All of the extra money he would get for having dependents would go to him. The only way you would see any of it, is if he gave it to you and it’s really not that much.
Also, in order for you to go to Japan with him, you would have to be married before he got orders to go to Japan. He would then have to apply for command sponsorship, which is basically asking for permission to bring his ‘family’ along. That can be denied. If he already has his orders for Japan, he could try to get them changed to include you after you get married, but they might not be able to do it. If you are not included on his orders to go to Japan, you will have to pay the cost of getting over there and getting any of the stuff you want to take with you over there. You will also have to have a passport before you could go.
It’s not as simple as saying you’re his wife and just going. Also remember airfare to get from Japan to the US is not cheap. The military will not pay for you to come home and visit friends/family or to come home if you decide you want to leave after a few months. That will all be on you.
Also, as @optimisticpessimist pointed out, adultery is a punishable offense in the military and some units are very strict about it. So the whole, if we meet someone else thing, could cause him some serious trouble if he’s caught being with other people while married to you. Also if you are dating around and being with other people, it could raise suspicions and that could lead to it being found out that it’s just a ‘contract marriage’.
Defrauding the government can get both of you in some trouble as well. Him more than you (I believe) and could cost him his military career (even lead to an dishonorable discharge) depending on his command at the time.
Also, and this is completely my own personal feeling, but if the command he is going to has only a limited number of command sponsorships that they can grant, and he gets it to bring you over, you would be keeping another family from being together during that service members time in Japan. I think thats really crappy and while you feel you won’t be hurting anyone else, you possibly could be.