A DWG file is in binary & zip format. A DXF file is nothing but ASCII text which uses far more bytes to store. So, yes, the DXF should be expected to be larger than the DWG....how much so will vary depending on the actual data in the DWG.
You can shrink it by ZIP'ing it up. I used the 3Dhouse sample drawing which is 1.72MB, saving as a R2007 DXF it is 6.94MB, ZIP'ing it brings it down to 1.05MB