B767 First Officer reported a high left engine vibration was felt after takeoff resulting in a return to the departure airport.

Narrative

After takeoff from ZZZZ we noticed a high engine vibration on the left engine from the N1. We continued to monitor the condition as we climbed which slowly got worse. It started around 3.2 and went up to 3.8 and we received three engine parameter reports on the printer. The captain transferred controls and radios to the first officer and called dispatch and maintenance. We talked with maintenance about what we were experiencing and he suggested it may be from ice but we informed that we had not flown through any precipitation. He suggested we reduce power to see if the vibrations would decrease and upon reducing the power the vibration got worse and increased to 5.0 on the indication. The flight attendants called to tell us they were experiencing a lot of vibration and noise in the back. We talked as a crew and with dispatch and maintenance and elected to return to ZZZZ. I informed the purser of the situation and approximate time to landing and made a PA announcement to the passengers stating we had high vibration in the engine and would return to ZZZZ for safety reasons. The first officer [requested priority handling] with ATC and we got vectors towards ZZZZ. We ran the overweight landing checklist after discussing the arrival and approach. The captain took back controls and I coordinated a gate with operations. We ran the descent checklist and verified with the purser that the cabin was ready for landing. We intercepted the localizer for XXR at 4000 feet and flew the ILS approach in visual conditions. The captain made an extremely smooth landing and the first officer informed tower that we would be taxing to our gate. We communicated with the fire trucks on a separate frequency that everything was okay and we would proceed to our gate. We parked and an agent came on and handled the deplaning process. We debriefed the flight and called dispatch and the chief pilot.