Anyone who tries to change the system will have to 'reckon with' me. = Anyone who tries to change the system will have me to 'reckon with'. [=I will oppose/fight anyone who tries to change the system]
She 'was reckoned' [='considered'] to be among the group's leaders. = She 'was reckoned' as one of the group's leaders.
When he won his first three matches, the other players realized that he was 'a force/man to be reckoned with'.
(..) This is so exciting! Sounds like kids to me. Sounds like kids to me. l want to get played with. Why can't time go faster? How many you reckon are out there? They sound so sweet. Look, everyone, it's nice here, l admit. But we need to go home. We can have a whole new life here, Woody. (..)2010 Toy Story 3