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'.
(..) someone who's given up! She's coming back. What's that with her? Neville! - How you look... - Like hell, I reckon. This is nothing. Seamus is worse. Hey, Ab! We've got a couple more coming through. (..)2011 Harry Potter and the Deathly Hallows: Part 2
(..) What happened? Well, he's angry... and scared too. He knows, if we find and destroy all the Horcruxes, we'll be able to kill him. I reckon he'll stop at nothing to make sure we don't find the rest. And there's more. One of them is at Hogwarts. What? You saw it? (..)2011 Harry Potter and the Deathly Hallows: Part 2