THE PLT FLEW THE ACFT TO AN ARPT WITH TWO TURF RWYS. RWY 5/23 WAS 2300' LONG & RWY 4/22 WAS 2600' LONG. AFTER ATTENDING A MEETING WHICH ENDED AT 1600 EDT, THE PLT ELECTED TO WAIT UNTIL LATER IN THE DAY TO TAKEOFF AFTER THE AIR HAD COOLED. SUBSEQUENTLY, HE BEGAN HIS DEPARTURE FROM RWY 5; HOWEVER, THE TEMP WAS STILL ABOUT 90 DEG, THE DENSITY ALT WAS APRX 2250' & THERE WAS A LIGHT WIND FROM THE SOUTH. WITNESSES RPRTD THAT AFTER LIFT-OFF, THE ACFT WAS IN A NOSE HI ATTITUDE, WHEN IT ENTERED A TURN TO THE RIGHT. SUBSEQUENTLY, IT COLLIDED WITH A TREE & CRASHED, APRX 200' EAST OF THE ARPT. NO PREIMPACT PART FAILURE OR MALFUNCTION OF THE ACFT WAS FOUND. A WEIGHT & BALANCE COMPUTATION SHOWED THE ACFT WAS LOADED APRX 36 LBS OVER ITS MAX GROSS WEIGHT LIMIT. AT 1853 EDT, THE WIND AT LEBANON, NH (APRX 15 MI SOUTH) WAS FROM 200 DEG AT 5 KTS. TAKEOFF COMPUTATIONS (ALLOWING FOR A TURF RWY & A 5 KT TAIL WIND) SHOWED 1492' OF RWY WOULD BE REQUIRED TO TAKEOFF & 2725' WOULD BE NEEDED TO CLEAR A 50' OBSTACLE.