Commercial Fixed Wing
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Time Pressure; Situational Awareness
Conflict Airborne Conflict; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Environment - Non Weather Related; Human Factors
Climbing out of ZZZ to FL380. Being very light and a slight wind shift; we went through FL370 at about 3;000 FPM. It went to altitude alert almost immediately before I could use vertical speed to arrest the rate. ATC gave us traffic at FL390 that we had in sight for a minute or so. The TCAS gave us the caution traffic then immediately a RA of level off. We leveled off at FL380 and traffic was at FL390.With our very light loads arresting climb rate needs to happen before a thousand feet.
Air Carrier Captain reported an altitude overshoot resulting in an RA.  The Captain stated the aircraft was very light in weight; which contributed to the event.