  Letting $T$ denote an ergodic transformation of the unit interval and letting
$f \colon [0,1)\to \mathbb{R}$ denote an observable, we construct the
$f$-weighted return time measure $\mu_y$ for a reference point $y\in[0,1)$ as
the weighted Dirac comb with support in $\mathbb{Z}$ and weights $f \circ
T^z(y)$ at $z\in\mathbb{Z}$, and if $T$ is non-invertible, then we set the
weights equal to zero for all $z < 0$. Given such a Dirac comb, we are
interested in its diffraction spectrum which emerges from the Fourier transform
of its autocorrelation and analyse it for the dependence on the underlying
transformation. For certain rapidly mixing transformations and observables of
bounded variation, we show that the diffraction of $\mu_{y}$ consists of a
trivial atom and an absolutely continuous part, almost surely with respect to
$y$. This contrasts what occurs in the setting of regular model sets arising
from cut and project schemes and deterministic incommensurate structures. As a
prominent example of non-mixing transformations, we consider the family of
rigid rotations $T_{\alpha} \colon x \to x + \alpha \bmod{1}$ with rotation
number $\alpha \in \mathbb{R}^+$. In contrast to when $T$ is mixing, we observe
that the diffraction of $\mu_{y}$ is pure point, almost surely with respect to
$y$. Moreover, if $\alpha$ is irrational and the observable $f$ is Riemann
integrable, then the diffraction of $\mu_{y}$ is independent of $y$. Finally,
for a converging sequence $(\alpha_{i})_{i \in \mathbb{N}}$ of rotation
numbers, we provide new results concerning the limiting behaviour of the
associated diffractions.
