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'.
(..) If I win, you do the road my way. Doc, what're you doin'? I don't mean to be rude here, but you probably go zero to sixty in, like, what? Three-point-five years? Then I reckon you ain't got nothin' to worry about. You know what, old-timer? That's a wonderful idea. Let's race. Gentlemen, (..)2006 Cars
(..) Now, May's expecting you up at the farm. You'll have no more trouble up there. Just green grass and fat cows. How are you doing? I'm getting there. I reckon you ought to connect the doohickey to the gizmo. Come here, you. You touch me with those hands and I'll rip you apart. No! (..)1979 Mad Max
(..) 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