  We successfully perform the three-dimensional tracking in a turbulent fluid
flow of small asymmetrical particles that are neutrally-buoyant and
bottom-heavy, i.e., they have a non-homogeneous mass distribution along their
symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect
the particle orientation along the preferred vertical direction and modify its
tumbling rate. The experiment is complemented by a series of simulations based
on realistic Navier-Stokes turbulence and on a point-like particle model that
is capable to explore the full range of parameter space characterized by the
gravitational torque stability number and by the particle aspect ratio. We
propose a theoretical perturbative prediction valid in the high
bottom-heaviness regime that agrees well with the observed preferential
orientation and tumbling rate of the particles. We also show that the
heavy-tail shape of the probability distribution function of the tumbling rate
is weakly affected by the bottom-heaviness of the particles.
