Personally I use PSD, not TIFF. One advantage that PSD has is that it is a compressed format by default, but using a lossless method of of compression, unlike JPEG. Using PSD is fine if you are only going to use Ps as your editing program. It is also possible to use compression with TIFF files too, and with TIFF you get several options, including JPEG if you really want. The most widely supported compression algorithm, and the one I would pick is LZW compression.
If you chose to keep all of the layers intact it is usual with both TIFF and PSD for the file to include and extra hidden layer, of the flattened image. This is done by using the maximise PSB option for PSD files, and is necessary when using other programs that understand PSD, including Lightroom. Lr doesn't do layers, and just uses the flattened layer. The extra layer is usually incorporated automatically in a TIFF when you have more than one layer.
Comparing the file size between a RAW file such as a CR2, and an uncompressed TIFF is never going to be an apples to apples comparison. The RAW file doesn't contain any encoded colour information, the RAW converter calculates the image colours based on knowing the colour response of the sensors RGGB Bayer Colour Filter Array. The sensor records a 14 bit value for every sensel location. At worse this may be stored as a full 16 bit value occupying two 8 bit bytes. When you convert to an RGB bitmap format like TIFF or PSD that gets converted to three values for each pixel, one red, one blue, and one green value. If this is saved as an 8 bit value of each colour you will need 3 bytes to store each pixel, so a 16 bit RAW will need only 2/3 the memory of an 8 bit RGB version. If you make the RGB values 16 bit, as you can with both TIFF and PSD, then you now need 6 bytes per pixel, rather than 2 for the RAW. This is for only a single layer image by the way. Additional layers of pixels will add the same amount of data again, although adjustment layers just save the info about the required adjustment, much like RAW edits are saved.
In addition for Canon CR2 files the image data is also compressed, again using a loss less compression system. I haven't looked at the specification, but I wouldn't be surprised to see that they used LZW, or a close variant of it.