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'.
(..) All right, everyone! Go back to your knitting. This is gonna be uncomfortable enough without all you nosy sods listening in. I reckon you have to be barking mad to put your own name in the Goblet of Fire. Caught on, have you? Took you long enough. I wasn't the only one who thought you'd done it. (..)2005 Harry Potter and the Goblet of Fire