The former King Arjit suggested marriage because he felt that was the quickest and easiest way to protect Yui from her crappy family. Even though Rodin did "purchase" her by legal means, her family would be able to contest it to force her to return. If Yui married into the royal family, there would be no contesting it.
Yui specifically says that Arjit isn't a lolicon and she understands that he's only offering marriage to protect her from her family.
Instead of marriage, they all come to an agreement to have Yui work as his official seamstress instead. That way she would still be under Arjit's protection (not as solid, but still better than nothing). Arjit apparently has been planning on taking down the Nielle family (Yui's family) for a while because they've been dealing with a lot of shadiness, so now he's thinking it's best if they somehow put Yui in charge of the Nielle family and do away with the rest.
The story continues on with Yui creating crazy OP clothes and armor...there is barely any romance in what I read. I think this story is focusing more on Yui's powers and politics than on any kind of romantic subplot. But by my guess, Arjit doesn't feel like the ML...IF there's going to be an ML, I feel it's most likely going to be a knight named Stall...or it's aiming for a harem-esque situation where there is no obvious ML.
Yui also mentions that she feels Arjit and Rodin are super handsome and cool, most likely because she is reincarnated and she's mentally their age inside. I know, I know, it's an excuse like the cliche 1000 year old loli in shonen ecchi animes, but at least in this case, the men aren't trying to sleep with her, they're genuinely concerned for her well-being. And judging from the comments on the WN forum, a lot of fans consider Arjit the "ojiisan" gentleman of the harem troupe.