We consider the Carleson embeddings from weighted Bergman spaces \(A^p_{\alpha }(\mathbb {H})\) over the upper half-plane \(\mathbb {H}\) into \(L^p(\mu )\) , where \(\mu \) is a positive Borel measure on \(\mathbb {H}\) . We characterize the r-summability of such operators for all \(p\ge 1\) , \(\alpha >-1\) and \(r\ge 1\) . In particular, the case \(p=1\) is solved, which was left open in He et al. (Adv Math 439:109495, 2024) in the setting of the unit disk. As applications, we show that for \(p\ge 1\) and \(\alpha >-1\) , there are no r-summing composition operators on \(A^p_{\alpha }(\mathbb {H})\) for any \(r\ge 1\) . Moreover, we obtain the description of r-summing weighted composition operators on \(A^p_{\alpha }(\mathbb {H})\) .
