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'.
(..) to come inside the fence... and bust up a chifforobe for her. She give me the hatchet, and I broke it up. And then she said... "I reckon I'll have to give you a nickel, won't I?" And I said, "No, ma'am. There ain't no charge." And I went home. Mr Finch, that was way last spring, (..)1962 To Kill a Mockingbird
(..) all the bluejays I wanted... if I could hit 'em. But to remember it was a sin to kill a mockingbird. Why? I reckon 'cause mockingbirds don't do anything... but make music for us to enjoy. Don't eat people's gardens. Don't nest in the corn cribs. They don't do one thing (..)1962 To Kill a Mockingbird