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'.
(..) You don't have any more vacations to sell. Why did you leave that ranch? Doctor, we don't have any more time for any of this now. But we don't reckon time the same way, do we? - This is all the time you'll ever have. - Later. Listen to me. We've only got five... No. I will listen now. (..)1991 The Silence of the Lambs