How does dropping ordnance affect the weight and balance of the aircraft?
the aircraft I worked on in the army were deadlined whenever 1% of total aircraft weight was removed, requiring either the part to be reinstalled or a total reweigh prior to next flight.


That's for internal equipment, which will affect the empty CG data.

All aircraft lose weight during a trip. Aircraft designed to lose a lot of weight all of a sudden ( C-5 airdrops, B-52 carpet bombing ) have the details and limits calculated during the design. In the case of bombers, the ordinance will be hanging near the wings and will have a specific release order, usually back to front. 

A tailgate aircraft dropping something will also have very specific procedures based on the weight of the pallet going out the back door. If it's delivering pizzas the procedure is along the lines of "whenever, dude". If it's a tank, it has to be positioned and locked down until the moment of release.

The above is very noticeable by the flight crew.

If the load stays (or gets stuck) on the back ramp, you're usually done. I used to skydive - 10 people on the back end of a smaller tailgate like a Casa can and do cause the plane to stall. The rules were stay at the front until it's your turn, then position and exit in a prompt manner. If the buzzer goes, let go NOW. Unlike a cargo plane, jump planes have 12,000 feet to recover from the stall.