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'.
(..) Have you room in your carriage for a dyin' man? I got no room for any Southern scum, alive or dead. Get out of the way! I reckon he'd rather try and walk it at that. Giddap! Jump, you gray-backed beggars! Act like they won the war! Now you come on and give me them pants, Mist' Kennedy. Come on. (..)1939 Gone with the Wind