I saw, on National Geographic, two well built navy guys lifting a *comparatively* small missile to be attached on wings of an F-18 Super Hornet.

So when one missile on left wing is launched doesn't it drastically shift CoG of jet? Who copes with this shift

1. Computer & other stuff internally adjusts the *zero* position of flight controls to attain level flight. In this case what is the basis of detecting shift in flight control made by pilot - the old zero or the new zero?
2. The pilot by shifting position of flight controls, using hands & feet, in *non-zero*ish positions to maintain level flight despite changed CoG. If yes, isn't it detrimental to pilot's performance in a dog fight?