CRJ-200 flight crew reported Gear Malfunction after takeoff.

Narrative

After takeoff from XXL in ZZZ; after gear retraction we received a Nose Gear Door Message and a Gear Disagree Message. Consistent with Landing Gear indications on ED-1. Captain and I called out the malfunctions on ED-1 and then Captain stated a short term plan; he transferred controls to me and said we should go back to ZZZ. I then took flight controls and complied with departure procedures while he [requested priority handling] and requested delay vectors. He identified this situation as a time threat and reaffirmed that ZZZ was the best place to land with rapidly changing weather conditions. I took radios and flight controls and set us up for an ILS and landing on XXL while Captain ran Quick Reference Handbook procedures simultaneously.Captain Quick Reference Handbook procedures resulted in gear eventually coming back down. We then determined that an overweight landing would be required and be best with the rapidly changing flight conditions; and because of this Captain decided to take flight controls for landing. We then landed following an ILS to XXL and taxied into the gate normally. Gear Malfunction resulting in nose gear not retracting on departure. No nose gear damage was noted on preflight. Aircraft had previously been flown from ZZZ1 with no issue.