How does mass affect bond stretching in UV spectroscopy?
In a very crude approximation, every bond can be considered to be a quantum harmonic oscillator. As you might know, the energies of such an oscillator are given by

$$ E_\nu = hc\omega_e \left ( \nu+\tfrac{1}{2}\right )$$

where $h$ is Planck's constant, $c$ the speed of light and $\omega_e=\sqrt{k/\mu}$. The constant $k$ is the force constant of the bond and $\mu$ is the reduced mass
$$ \mu=\frac{m_1m_2}{m_1+m_2}$$
So if you increase the mass of one of the particles, while $k$ stays roughly the same, $\omega_e$ becomes smaller and the energy spacing between the vibrational levels decreases.