报 (traditional 報) originally showed a hand subduing a kneeling figure — announcing a verdict. From delivering judgment to delivering news: the report, announced by hand.
报 delivers: 报纸 (newspaper), 报名 (sign up — 'report your name'), 天气预报 (weather forecast), 报告 (report). Its deepest sense is 报答 (repay kindness) and 报仇 (avenge) — the Chinese moral ledger where every favor and every wrong must be 报-ed back. 善有善报 — good deeds get good returns: karma keeps the books.
A hand 扌 delivering the announcement — REPORT (and repay).
善有善报，恶有恶报 — 'good has good returns, evil has evil returns' — the folk law of moral accounting.