MD80 DIVERTS TO NEARBY ARPT ACCOUNT VIBRATION.

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DURING CLB TO MID LEVEL ALTS; WE FELT A VIBRATION WITHOUT ANY ACCOMPANYING ABNORMAL INDICATIONS. WE ALSO GOT A TAIL COMPARTMENT TEMP HIGH LIGHT. AFTER THE RED BOX ITEMS AND WHILE RUNNING THE QRH CHKLIST; THE LIGHT WENT OUT SHORTLY AFTER THE FIRST FEW STEPS. THE FLT ATTENDANT ALSO CALLED AT THIS TIME TO DESCRIBE THE STRONG VIBRATION FELT IN THE CABIN. EVEN THOUGH THE VIBRATION INITIALLY DIDN'T SEEM TO FOLLOW THROTTLE MOVEMENT; DIALOG WITH THE FLT ATTENDANTS AND FURTHER THROTTLE MANIPULATION SUGGESTED A PROB WITH THE R ENG. WE TOLD ATC WE WERE WORKING ON A FEW ISSUES AND ALERTED THEM TO A POSSIBLE DIVERT. THE FO'S INPUTS AND SUGGESTIONS WERE VERY HELPFUL DURING THIS EVENT. I INSTRUCTED THE FO TO FLY; TALK; AND PREPARE FOR A DIVERT WHILE I TALKED WITH THE FLT ATTENDANTS; PAX; AND DISPATCH. DISPATCH SUGGESTED ZZZ WAS A CLOSER DIVERT CHOICE. I AGREED WITH HIS SUGGESTION. WE DECLARED AN EMER; DIVERTED TO ZZZ; REVIEWED SINGLE ENG AND OVERWT LNDG PROCS. I LANDED THE ACFT AT 1500 LBS OVERWT. WE TAXIED TO THE GATE AND BRIEFED MAINT.