The AIM-120 weighs in at about 335lb (152kg), and the AIM-9 at about 190lb (85kg). While heavier, the Stores Management System (SMS) and the Fire Control Computer (FCC) know what is installed where, and compensate/adjust flight characteristics as needed.
You put the most capable missile, the AIM-120, out the outboard stations. You'd use that first. Only later might you want to use the shorter range AIM-9.
So, if you were to shoot the AIM-120 from Sta 2 (left inboard), you'd still have the AIM-9 out on the wingtip.
Do it the other way around.
Also, the AIM-9 since the AIM-9G can slave the missile seeker head to the aircraft radar. Target acquisition is not solely dependent on the IR in the missile and line of sight.
The AIM-9G was the first version to include SEAM (Sidewinder Expanded Acquisition Mode), basically an improved AIM-9D seeker head, but was quickly made obsolete by the AIM-9H. The latter was the first model to offer limited all-weather capability, as well as solid-state electronics and double-delta control surfaces resulting in a superior maneuverability compared to older models. SEAM slaves the seeker head of the missile to the radar when in "dogfight" mode, which enables the seeker head to be uncaged, slewed toward a specific target by the aircraft radar, and made to track that particular target before being launched.
(from F-16.net - http://www.f-16.net/f-16_armament_article1.html)