  We measure weak quasiparticle tunneling across a constriction in the second
Landau level. At $\nu$ = 7/3, 8/3 and 5/2, comparison of temperature and DC
bias dependence to weak tunneling theory allows extracting parameters that
describe the edges' quasiparticle excitations. At $\nu$ = 8/3, our results are
well described by a particle-hole conjugate Laughlin state, but not compatible
with proposed non-Abelian quasiparticle excitations. For $\nu$ = 5/2, our
measurements are in good agreement with previous experiments and favor the
Abelian (3,3,1) or (1,1,3)-states. At these filling factors, we further
investigate the influence of the backscattering strength on the extracted
scaling parameters. For $\nu$ = 7/3, the backscattering strength strongly
affects the scaling parameters, whereas quasiparticle tunneling at $\nu$ = 8/3
and 5/2 appears more robust. Our results provide important additional insight
about the physics in the second Landau level and contribute to the
understanding of the physics underlying the fractional quantum Hall states at
$\nu$ = 7/3, 8/3 and 5/2.
