While I will not rule out it being tail heavy, the engine could also be setting with some down thrust so that when you slow down and idle back, the tail drops. What happens when you fly inverted? Does it climb?
ORIGINAL: Fighterpilot
it will drop the right wing if too much elevator is applied and it tends to fly tail down and drop like a brick when power is reduced. It is balanced wing tip to tip, so I do not have a heavy wing.