First Officer reported excessive trim was required to maintain control of the aircraft. The Flight Crew elected to divert to make an overweight landing.

Narrative

While conducting preflight checks I initially noticed the rudder trim set at 5 degrees left. After re-centering the rudder trim I asked the Captain if he had moved it there for some reason and said he did not. During the Before Takeoff Checklist we reconfirmed per the checklist that all trims were set to appropriate settings and rudder and aileron trim set both to 0 degrees. After liftoff the airplane was greatly out of trim and started to trim left rudder almost to 7 degrees left and ailerons 2 degrees (approx) left. During climb out trim was not getting any better and continued to manually fly the airplane. Captain engaged autopilot and aircraft tried to trim with about 7 deg left yoke position. Decided to trim out the aircraft a little more to 7 degrees left rudder.We discussed potential hazard considerations such as an engine failure with the possibility of running out of trim as our worse case and decided to [request priority handling] due to flight control malfunction and rigging. Diverted to ZZZ and landed overweight at 170;200 pounds (limit 157.3 lbs.) and landed smoothly. Emergency services confirmed brake temps were within normal limitations and was cleared to gate. We wrote up over weight landing and flight control trim rigging with explanation with local Maintenance. As we made the decision to divert the Captain alerted [maintenance]; Dispatch; ATC; Flight Attendants; and PAX and we maintained great communication with all agencies involved. ZZZ was great with coordination and securing new aircraft and gate for us to remain with PAX to continue to ZZZ1.