As a part-yea resident, you will pay taxes according to where you actually worked, so you have to allocate 1/3 to Virginia and then 2/3 to Delaware. The amount on your W2 Box 15-16-17 is based on where the withholding was taken- so since your company did not switch over to Delaware, you paid into Virginia all year. (Your refund from Virginia in theory should be close to the amount you owe in Delaware depending on the state tax rate of course.)
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