CE680 Captain reported unusual engine vibration resulted in diversion.

Narrative

When finished clearing customs in ZZZ after a passenger flight; we walked out to the aircraft and noticed storms approaching the airfield. The winds were beginning to pick up and I wanted to get the airplane back to the FBO before the downpour kept us trapped in the airplane on the FBO ramp. Person A my partner had also mentioned that the winds were picking up. We ran the normal start checklist and began a right engine start. It seemed like right around the time of pushing the start button; rain started pouring down and wind gusts increased. At about 5 or 6% N1; the N1 stopped increasing and I immediately aborted the start. No limitations were exceeded; the Interstage Turbine Temperature (ITT) never went past the straight up vertical point on the gauge. Approximately; 15 minutes later; the storm had passed and winds died down. We attempted another engine start and both engines were started without event. We taxied to the FBO and shut down. All engine indications at that point were normal. After we boarded the passengers; We started both engines and taxied to Runway XX for take-off. Because we were so heavy; I decided to do a static take-off and ran both engines to full power before releasing the brakes. All indications were normal. We took off and began climbing. All indications were normal. We had to deviate around some weather that was north of ZZZ and continued the climb. At approximately 21000 ft; Person A; my partner said they heard a slight noise which I didn't hear. They had regular headsets and I had ANR headsets. Then we began to feel a very slight vibration. We began to talk about leveling off to figure out what was causing the vibration. Then the noise got louder and the vibration grew to a moderate vibration. I asked Person A to request a level off and we spoke about diverting. The passenger came up to the cockpit and expressed concern so we decided to go to the closest airport in the interest of safety. We knew we were overweight and I made the decision to get the aircraft on the ground without holding. We landed in ZZZ1 uneventfully and taxied to the FBO. Upon exiting the aircraft and on postflight; we noticed what looked like scrape marks on the inside of the right engine where the fan blades turn at approximately the 10 o'clock position. I went inside of the FBO to call maintenance. I told them we diverted due to vibration and unexplained noise. During the conversation; I told maintenance about the aborted start in ZZZ and that winds suddenly started gusting. I was concerned that the two might be related. I told maintenance that no indications were exceeded and there was no hot start. They said; they were sure that the aborted start had nothing to do with the vibrations. I wrote up the aircraft per the discussions with maintenance and we sat with the passengers on the airplane until the recovery arrived.