  We prove sectorial extension theorems for ultraholomorphic function classes
of Beurling type defined by weight functions with a controlled loss of
regularity. The proofs are based on a reduction lemma, due to the second
author, which allows to extract the Beurling from the Roumieu case, which was
treated recently by Jim\'{e}nez-Garrido, Sanz, and the third author. In order
to have control on the opening of the sectors, where the extensions exist, we
use the (mixed) growth index and the order of quasianalyticity of weight
functions. As a consequence we obtain corresponding extension results for
classes defined by weight sequences. Additionally, we give information on the
existence of continuous linear extension operators.
