Date: 202101
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: Icing
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Climb
Airspace: Class B ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: First Officer; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Confusion
Second reporter function: Captain; Pilot Not Flying
Anomaly: Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance
Detector: Automation Air Traffic Control; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance
Contributing factors: Environment - Non Weather Related; Human Factors; Aircraft
Primary problem: Human Factors

Narrative: 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.


Second narrative: 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.


Synopsis: Air carrier flight crew reported an overshoot of altitude on departure and made reference to the aircraft being light in weight.