CE750 First Officer reported a fuel imbalance issue during cruise. The crew troubleshot the problem but were not able to resolve it and continued to the destination airport landing with a fuel imbalance of 500 pounds heavy on the left side.

Narrative

On Day 0 my Captain and I departed from ZZZ to ZZZ1. After level off at cruise altitude; the aircraft Crew Alert System (CAS) message alerted 'Wing Tank O'Full R'. This indicated overflow of fuel from the center tank to the right tank and created a fuel imbalance (heavy on the right side) as well as right wing tank fuel draining from the right overfill vent into the atmosphere.To address and correct the problem; we complied with the aircraft's emergency and abnormal procedures manual by flipping the Center Wing Transfer Switch to 'Off' to maintain a proper fuel balance. When placing the switch in the 'off' position; we were then alerted with 'CTR XFER XSIT R' CAS Message indicating the center tank transfer valve did not close as commanded. The Center Wing Transfer valve was neither open nor closed and was stuck in transit. As a result; fuel flow to the overfilled right wing continued and fuel imbalance did not terminate. Then; to combat the continued fuel balance issue; my Captain and I tried to even the fuel tanks by utilizing the crossfeed selector to eliminate the fuel imbalance. Instantly upon utilizing the crossfeed selector; we were presented with 'FUEL MOTV FAIL R' indicating the respective fuel motive flow shutoff valve has failed to close when crossfeed has been selected. Crossfeed from the opposite tank will not occur. Fuel will continue to feed from the affected tank. Center Wing Transfer Switch and Crossfeed Methods to even the fuel imbalance both failed. Using our last resort; turned the gravity crossflow switch to 'On' to allow fuel to flow from right tank to left tank to allow fuel to equalize between the two tanks by gravities force. The gravity crossflow method did seem to slow the rate at which fuel was becoming imbalanced. I advised and suggested that we deviate to various alternate airports as we progressed to our destination airport. My Captain did not agree and insisted we continued to our destination airport. Upon landing the aircraft; we had a fuel imbalance of 500 lbs heavy on the left side. After landing; the Captain refused to write down the mechanical irregularities in the maintenance logbooks. He advised that we would continue flights the next day as planned and would respond accordingly to how the plane performed. I called the Chief Pilot and communicated the events that took place during the flight. He stated that if I do not feel safe flying the airplane then that is my decision. However; he also advised that performing maintenance would not be possible since the aircraft was now located in ZZZ1. We were either to fly the passengers to ZZZ2 the next day; or he could attempt to coordinate a reposition flight for us the next day to a maintenance base. Considering I did not feel safe flying the aircraft with or without passengers prior to the aircraft being inspected by maintenance first; I decided not to fly the aircraft the following day. I also chose to resign from the company as my Captain and management have made decisions that are not in the best interest of safety for flight crew or passengers.