Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Confusion
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance
Environment - Non Weather Related; Human Factors; Aircraft
With a light load (XX passengers); Tower cleared for an expedited takeoff Runway XXL; Runway heading. Takeoff without incident; with a high climb rate due to weight. Configured and continued climb hand flying. Reaching 3;200 feet; at 200 knots; climb rate was 4;000 FPM+; leveled a bit to slow climb and increase speed to 250 knots.  Captain was completing after takeoff checklist; and made 1;000 foot call. Reached 250 knots at 4;200 feet; and proceeded to slow and increase climb simultaneously; while ATC was giving further clearance. In my mind I expected a further climb; but we only received direct ZZZZZ. Realizing we were not getting cleared higher; and at 4;600 feet with an increasing climb rate currently at 3;500 FPM; I immediately began correcting with pitch and power. Captain said watch your altitude; and I advised correcting. ATC advised maintain 5;000 feet; Captain responded correcting. The stable correction required a top altitude of 5;300 feet. ATC advised no problem; and that there was overhead traffic. There was no disruption to traffic or flight due to this 300 feet deviation. The rest of the flight was conducted without incident.I believe I slowed my deceleration in order to level at 5;000 feet when I heard ATC begin giving further clearance because I just expected higher to be given also. Obviously each clearance is specific; regardless of expectations; so pitch and power accordingly; and a correction won't be necessary. It didn't help that the climb rate was very high due to light load; adding hand flying to it just increased the workload. At light loads; in the busy ZZZ environment; probably best to utilize the automation a bit more to lighten the workload.
During initial climb via the ZZZZZ departure as I was completing the after takeoff checklist I noticed we were at a very high rate of climb as we were approaching our top altitude (maybe 4;800 feet) and reminded name (FO) of our 5;000 assigned altitude he immediately started correcting. As a result of the rate of climb we climbed through 5;000 feet to 5;300 feet and then back down to 5;000 feet. This happened during a busy time I was running checklist and communicating with ATC while the FO was hand flying. I feel that I could have paused the checklist from the 1;000 feet horn and call until our altitude was captured to make sure we wouldn't climb through.
Air carrier flight crew reported an overshoot of altitude on departure and made reference to the aircraft being light in weight.