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'.
(..) blowing in the wind. Well, Rose, we've walked about a mile around this boat deck... ..and chewed over how great the weather's been and how l grew up,... ..but l reckon that's not why you came to talk to me, is it ? - Mr Dawson, l... - Jack. Jack. l want to thank you for what you did. (..)1997 Titanic