From Fermi's Golden Rule one can derive that the decay rate for a two-particle decay ($A\to B+C$) is given by
$$\Gamma = \frac{p^*}{32\pi^2m_A^2} \int |{\cal M}|^2 d\Omega,$$
where the absolute value of the momenta of the outgoing particles is given by
$$p^* = \frac{1}{2m_A} \sqrt{\left[ m_A^2 - (m_B + m_C)^2 \right] \left[ m_A^2 - (m_B - m_C)^2 \right] }.$$
$\cal M$ is the matrix element, and $m_{A,B,C}$ are the masses of the particles involved. (This is textbook knowledge, cf. Griffiths, Thomson, or Wikipedia.)
Now the lifetime of a particle is given by $\tau = 1/\Gamma$, and from the above equation we should be able to tell how the lifetime goes with the mass $m_A$ (assuming $m_{B,C}$ stay constant).
For $m_A \gg m_{B,C}$, we get $p^* \sim \frac{\sqrt{m_A^4}} {m_A} = m_A$, thus $\Gamma \sim \frac1{m_A}$ and $\tau \sim m_A$, i.e. heavier particles live longer than light particles.
Where have I gone wrong?