Flight Crew Multiengine; Flight Crew Commercial
Flight Crew Last 90 Days 120; Flight Crew Total 4200; Flight Crew Type 250
Workload; Distraction; Situational Awareness; Confusion
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Loss Of Aircraft Control; Inflight Event / Encounter Fuel Issue
Flight Crew Regained Aircraft Control; Flight Crew Diverted
Human Factors; Aircraft
Approximately 300 nm ENE of ZZZ at about XA30Z we were at FL430 enroute.  We had established ourselves level at .70 and had then set the power to 93.0%; in line with the altitude and temp (ISA -2c) for long range cruise according to the book.  We were expecting .70 mach and fuel flow of 750 lbs/hour.The flight profile from ZZZ1 to ZZZ2 was doable on the Long Range profile per the book with the fuel load we took; but we were closely monitoring the remaining fuel at destination and the nm/gal fuel.The plane began to slowly react to the 93.0 power setting with pitch increasing and speed slowing.  This was quite gradual; perhaps a  IAS/minute.  At 8 degree nose up pitch; 160 IAS and about .62 mach the autopilot disengaged.  This was followed by a stick shaker.  I pitched level and added full power.  The PIC took aircraft controls at this point.  In this recovery we lost 1;000 feet and recovered positive control at 420.We were unsurprisingly busy during this roughly 1 minute period and did not advise ATC that we were having an in flight emergency and descending.  ATC called as we reestablished altitude control and warned us to return to 430.  At that time I advised that we had an in-flight emergency due to a stick shaker and were now stable at 420 but unable to climb. ATC urged us to climb due to an approaching aircraft at 410. We were unable to do so; advised ATC and told them were were turning right to avoid.  At the same time ATC turned the conflict traffic left.  Shortly thereafter both aircraft received an A.  We advised ATC we were unable to respond to our RA with a climb; the other aircraft did respond to theirs with a descent.  Of note; while the RA needed to be addressed; we were level at 420 and there was no common altitude at any time closer than 1;000 feet.After the conflict resolution; we requested/descended to 400.  We subsequently decided to divert to ZZZ for fuel.  The balance of the flight was without incident.We were asked to call Center and did so after the flight was completed.  The Center Supervisor (not sure of his title) said he would not record this as a pilot deviation as we were responding to an in flight emergency.  This was backed up by our radio transmissions at the time.We were monitoring performance the entire time and were discussing whether to add power or to see if the plane could accelerate back to book numbers on its own.  During the subsequent week we monitored fuel levels in the aircraft vs indicated; and now believe that we may have been overweight by about 400 lbs.  This would explain the performance issue.The Company is looking into this possible gauge discrepancy.  In the meantime; we are using the estimated higher weight in all WB and performance calculations; but the lower indicated amount for flight duration; essentially adding 400 lbs to BOW until the gauges are re calibrated.
Beechcraft 400 First Officer reported an airspeed degradation while flying a Long Range Cruise profile at FL430; resulting in an inability to maintain assigned altitude.