  We propose iterative inversion algorithms for weighted Radon transforms $R_W$
along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x,
\theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics
in $\theta$ and assuming that the zero order term $w_{0,0}(x)$ is not zero at
any $x \in R^3$ , we reduce the inversion of $R_W$ to solving a linear integral
equation. In addition, under the assumption that the even part of $W$ in
$\theta$ (i.e., $1/2(W (x, \theta) + W (x, -\theta))$) is close to $w_{0,0}$,
the aforementioned linear integral equation can be solved by the method of
successive approximations. Approximate inversions of $R_W$ are also given. Our
results can be considered as an extension to 3D of two-dimensional results of
Kunyansky (1992), Novikov (2014), Guillement, Novikov (2014). In our studies we
are motivated, in particular, by problems of emission tomographies in 3D. In
addition, we generalize our results to the case of dimension $n > 3$.
