An LR55 flight crew noticed birds on takeoff roll and experienced failure of their landing gear to retract after takeoff.

Narrative

That day the weather at that airport was VFR. While taking off from runway XX; I saw birds on the runway coming our direction. We took off and while airborne we could not retract our landing gear. We recycled the gear another time without success. The Captain called Tower Control and advised that he wanted to remain with them for a while because we had to fix a landing gear problem. Tower Control asked us if we wanted to come back and land. The Captain answered that we could not land because we were exceeding our maximum landing weight. Then the Tower Control told us to switch to the Departure frequency and told us to advise them about our intentions to divert. While departing we declared an emergency because we had to burn fuel and also because we couldn't retract the gear. After the Captain determined that we could not land; we advised the passenger that we had to divert. We burned the fuel to meet our maximum landing weight and we diverted to a suitable airport. We stayed VFR during the entire flight and we landed safely to ZZZ.