As others have pointed out, the Navy will move your stuff up to a weight allowance (around 10,000 lbs for an ENS, IIRC). If your stuff is under that limit, then you are good to go and the move will not be any more or less painful, it will just have an extra pack-out day or two.
The more concerning part should be your ability to find a large enough place to fit your stuff in some duty stations. For example, if you are stationed in San Diego or Pearl, you are not going to afford a 3- or 4- BR home with a basement and attic for all that stuff on ENS BAH.
Another thing to consider is that you bought all that stuff for a reason. Unless you picture never wanting it again, you might want to consider long-term storage instead of re-buying stuff down the line after selling it for a small fraction of its value.
You will most likely lose money if you do a full DITY move, since unlike movers you don't own your own truck. Do a partial DITY: Movers come and pack out all of your major stuff, you get weight tickets for your car and pack it full with clothes, uniforms, irreplaceable valuables, and whatever else you can fit in there. You'll get a few hundred dollars for stuff you have to take with you anyway, and the Navy moves the rest of your stuff (relatively) hassle-free. If the movers break/damage anything, you file a claim and get reimbursed for it.