The 3rd Prince is burdened because he was born into a prestigious royal family without enough ability to back that reputation. He managed to make contract with two spirits, but unlike Yuri, his are just low level spirits. People also keep comparing him with his brothers (who never even got mentioned by name in the story). He tried to put an act, although people still think it's fake because he got no power.
Bridgette changed his life. He was just curious about this girl who is even more pathetic than he is. A girl born into one of the four prestigious nobilities, but only managed to make contract with nameless spirit, and got her hand burned by her own father, then chased out of the main house. Bridgette loves him and will do anything he says. People also think better of him now for being a kind prince who showed mercy to that worthless girl.
But it really change as he knew Bridgette more. He found out she's actually very smart. As eldest daughter of the Earl of Fire's house, she will be sent to the Royal Academy. It's not a matter of choice, it will smear the family reputation if the parents deny her from attending. When that day come, people will find out Bridgette is actually smart and superior to her fiance, making him pathetic again. This is why he told Bridgette to pretend stupid and arrogant, so he will always be better.
The last straw is when he found out, her contracted spirit is the legendary Phoenix. The spirit stay asleep all the time as even with Bridgette talent, it's still too powerful for her. It's why the spirit got misidentified as nameless and never answer her call. That's it, when the world founds out, Bridgette will become famous, while everyone see him as inferior. He start to look for another choice, another stupid girl.
Lisa still can't accept Bridgette's achievement. In the next test (searching for spirit stones in forest), the Prince provoked her to attack and burn Bridgette. The attempt failed. Lisa tried to accuse Bridgette, by burning her own hand. But Undine, Yuri's spirit, stand as witness. Lisa locked herself in her bedroom since that day.
Joseph had enough with Lisa too. Bridgette is daughter of a famous family. Even if practically disowned, she's still educated in manners. Bridgette's haughty act only hurts her own reputation, while giving the Prince a good reputation for being kind even to that kind of fiance.
Lisa in the other hand, is from the lowest rank of nobility. She shamelessly flirt with him in public and talk like her words are Joseph's. Fancying her demand will just ruin his own reputation, so he keep avoiding to announce engagement to Lisa. But the girl is too persistent. He need to dispose her.
Joseph came to offer another engagement with Bridgette, thinking she will gladly accept it. But Bridgette straightly refuse him in front of the other students, saying she already got another man she loves (and pulled Yuri out with her).
In the next part, the Church became interested because there's news about Bridgette's "nameless" managed to neutralize a raging Aerial (wind spirit, not Gundam). There's also accounts about pillar of light from her mansion (when she managed to call her contracted spirit out). They took chance in a scheduled review, where staff from the church are interviewing the students about relationship with their spirit, to get to see her closer without making it look like special investigation. Bridgette, after overcoming her trauma of fire, managed to summon her spirit, who shows up as a tiny fluffball chickling who is really afraid of Kira (her family is poor, so she often told that bird about how she likes to eat chicken, fat chicken).
Joseph, colluded with the botany teacher to lock Bridgette. He plan on using a magic item that can sever contract. It's used by the church to help people who inadvertently contracted harmful spirit, and the use is very restricted because no spirits would want to make another contract with people touched by that. He thought, everyone including Yuri likes Bridgette because she has a powerful spirit. If she lost that, then she will return into the pathetic girl who can only depend on Joseph.
The attempt failed, so Joseph had enough and plan on double suicide. Bridgette's spirit saved them, and one of Joseph's spirit use the magic item to sever its contract because it had enough with Joseph's behaviour. Their kingdom revere the spirits, so having a spirit go as far as "divorcing" their contract means that person must have been really horrible.
Other than the assault and arson, Joseph is also apprehended for illegally using items that shouldn't be brought out of the church. The bishop who helped him (the priest who misidentified Bridgitte's spirit as "nameless" years ago), and the botany teacher, are also apprehended.