I could be wrong but I think it's because the structure of diethyl is much larger than water. So we know it'll occupy a larger volume than water. so evn though the ether is heavier than water but because the volume is higher as well ether will have a lesser density.
Volume would also depend on the degre of Hydrogen bonding. A molecule of water can form 4 H-bonds but in an diethyl ether cann't form bonds with itsef. So water packs more closely together with other water molecules and therfore taking up smaller volume.
Density =mass/volume
for diethyl it's 0.713 g/ml an for water it's 1.0g/ml