  We present an experimental system for Rydberg tweezer arrays with ytterbium
(Yb) atoms featuring internal state manipulation between the ground ${}^1$S$_0$
and the metastable ${}^3$P$_2$ states, and single-photon excitation from the
${}^3$P$_2$ to Rydberg states. In the experiments, single Yb atoms are trapped
in two-dimensional arrays of optical tweezers and are detected by fluorescence
imaging with the intercombination ${}^1$S$_0 \leftrightarrow {}^3$P$_1$
transition, and the defect-free single atom arrays are prepared by the
rearrangement with the feedaback. We successfully perform high-resolution
${}^1$S$_0\leftrightarrow {}^3$P$_2$ state spectroscopy for the single atoms,
demonstrating the utilities of this ultranarrow transition. We further perform
single-photon excitation from the ${}^3$P$_2$ to Rydberg states for the single
atoms, which is a key for the efficient Rydberg excitation. We also perform a
systematic measurement of a complex energy structure of a series of D states
including newly observed ${}^3$D$_3$ states. The developed system shows
feasibility of future experiments towards quantum simulations and computations
using single Yb atoms.
