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'.
(..) The Sheriff will hear of this! I truly hope so. Buy yourself a new sow. God bless you, Fanny. And God bless Robin Hood! We reckon he's nicked... ...three to four million in the last five months. Raise the bounty on his head. crowns. Begging your pardon, (..)1991 Robin Hood: Prince of Thieves
(..) You must fight me for it. Love to, mate. Be careful, Father. He walloped of the Sheriff's men. Is that so? Reckon I'll enjoy this. He's your father? He's drowning! Lost something? Thanks for the taxes. The rich boy's lost for words! (..)1991 Robin Hood: Prince of Thieves