Patrick and Archie share a relationship that evolved from a friendship into an actual relationship. Their love of Quidditch is what caused them to talk, and eventually created a bond between them. The two of them started to hang out more together and talk about other stuff as well and it even went so far that they invited each other over during the holidays.
Archie started to develop feelings for Patrick during their third year, but at that time Patrick was already in a relationship with Theo Raeken. He kept his distance, not wanting to be the cause of why their relationship ended, just so he could have Patrick for himself. However, when the opportunity presented himself after Patrick and Theo got into an argument and broke up, Archie made sure to give Patrick all his attention and to be a shoulder to cry on.
After his relationship ended, he started spending even more time with the Gryffindor boy and, in time, started to feel something for Archie as well. In a bar in Hogsmeade which they visited in their fifth year, Archie confessed his feelings for the Hufflepuff and was happy to hear that he felt the same. They fell into a relationship that eventually was put under pressure after it was revealed that Archie alongside his gang Alec Tate and Jesse Bullock, went after Brody Hudson and Scott McCall for more than a year. Patrick told him that he wouldn't dump him if Brody and Scott could both forgive him for what he did. Thankfully for Archie, they did so Patrick didn't end the relationship.
They started a relationship in 1995, started living together in 2000, and in 2005 Archie asked Patrick to marry him, to which he said yes. However, with Theo presumed dead, they didn't expect to see the Slytherin turn up at their wedding, right before they were about to say their wedding vows. After it was explained by Head Auror Brody what happened to Theo during the First Wizarding War and how he had ended up in Azkaban, everyone believing he had died during the Battle of Hogwarts, Patrick couldn't continue with the wedding and broke it off, ended his relationship with Archie and went back to Theo.
Second Year (1992-1993)
Patrick met Archie at the Great Lake during his second year. Patrick had received the news that he was accepted into the Hufflepuff quidditch team as a Chaser and was just sitting down in front of a tree at the lake to relax after his thorough audition. He was minding his own business when all of the sudden this Gryffindor boy walked up to him, informing him that he saw him on the Quidditch field during his audition and that he was watching from the stands, and that he wanted to compliment him for making the Hufflepuff team, declaring that they'd be rivals when their Houses faced each other on the fields. Also a Chaser, Archie did, unbeknownst to his teammates, give Patrick tips and tricks best suitable for a Chaser, and it was the start of their friendship.
Patrick and Archie kept meeting with each other before and after a Quidditch match but only if one of their Houses (or both) played, wanting to wish each other luck beforehand and then afterwards, congratulating the winner. For the remainder of the 1992-1993 school year all of their interactions were related to Quidditch in one way or another.