When I have a node running, lets say an Entry Guard, that also acts as a Directory Mirror. Will the bandwidth used sending directory information also count towards the consensus weight?
And if so or if not so, what is the reason behind this?
No it does not. (..and neither does the OR traffic.)
The idea that 'traffic counts towards consensus weight' is not how it works. As I understand (from the linked document), the bandwidth is measured by building a circuit through the relay and transferring a file through it (and measuring how long that takes). So the consensus weight is not determined any amount of traffic (neither OR nor DIR) that the relay reports, but by periodic bandwidth measurements from Bandwidth Authorities.
See Bandwidth Scanner specification especially section 1.4, 1.5