  It is shown that the coordinate algebra of the quantum $2n+1$-dimensional
lens space $\mathcal{O}(L^{2n+1}_q(\prod_{i=0}^n m_i; m_0,\ldots, m_n))$ is a
principal $\mathbb{Z}$-comodule algebra or the coordinate algebra of a circle
principal bundle over the weighted quantum projective space
$\mathbb{WP}^n_q(m_0,\ldots, m_n)$. Furthermore, the weighted $U(1)$-action or
the $\mathbb{CZ}$-coaction on the quantum odd dimensional sphere algebra
$\mathcal{O}(S^{2n+1}_q)$ that defines $\mathbb{WP}^n_q(1,m_1,\ldots, m_n)$ is
free or principal. Analogous results are proven for quantum real weighted
projective spaces $\mathbb{RP}^{2n}_q(m_0,\ldots, m_n)$. The $K$-groups of
$\mathbb{WP}^n_q(1,\ldots, 1, m)$ and $\mathbb{RP}^{2n}_q(1,\ldots, 1,m)$ and
the $K_1$-group of $L^{2n+1}_q(N; m_0,\ldots, m_n)$ are computed
