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Sounds like you are resizing without resampling. The pixel dimension:resolution ratio is staying the same. So you can resize something that is 720px x 720px @ 72dpi to 360x360 @144dpi and the image will have the same file size.
Resampling will keep the resolution the same while reducing the number of pixels, so your file will go from 720px x 720px @ 72dpi to 360px x 360px @72dpi.
When you reduce an image's dimensions by half, the file size is usually reduced by more than half, I think it has something to do with math... like an inverse square law or something.
Part of the problem is in the terminology, resizing can mean file size, image dimension, adding starch.
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