Ok thanks for your comments, I have found the cause.
The *unexpected* large file size is caused by the layers I use for adjusting the colors. I use the methods descibed in the book "Photoshop for digital photographers". There are three layers used, one for the blackpoint, one for the whitepoint and one for neutral grey. Then I use "Curves" to adjust the colors.
When I delete these layers after color correction, the file size is about 40mb for 16bit and 20mb for 8 bit data, which is the expected file size.
Is it common to use any kind of compression when saving a tif file? I notice when I use LZW the file size is only reduced when saving as 8 bit per channel. When saving at 16 bit using LZW compression the file size becomes larger...