Hayato's first impression of the new kid (babysitter) was WIMP. He looked like someone that the kids would normally bully. That's why he hadn't really bothered to talk to him. At first.
He was amazed when the boy effectively made all of the kids his friends, more so when he made them obey his rules. Ryuuichi had done a feat that even the NEET (Usaida) had taken a week to do. Truly, an amazing man that he is.
To be frank, Hayato had planned to join the Babysitter Club, even before Kotarou had dragged him in. The kid was quite interesting in the first place. All more when he had the guts to talk to him in class. Only a few can, and did, after all.
By then, Hayato knew that he'd enjoy being a friend of Ryuuichi. Ryuu, in all honesty was cute. He had shown Hayato faces and habits that are quite girly. It was quite disconcernting at first, since he did not know why he was blushing (despite himself) when Ryuu was being cute. But he found it out, one day, while he was staring at Ryuu's ass. It may have been a shocking revelation, but he found that he doesn't really care. He wasn't the first one to fall for Ryuu, after all.
He had overheard a certain conversation of his classmates saying that a good portion of the class already harboured feelings for Ryuu. Well, who wouldn't? Ryuu is kind, sweet, caring, and humble after all. He was also quite intelligent, which is a bonus point. Needless to say, Ryuu is a perfect example of a "Boy-Next-Door". Even kids love him. Ryuuichi is a perfect babysitter through and through.
That's why, who can't blame him for being a little gentler to Ryuuichi? It was already a given that he'd make Ryuuichi his. You can't blame him for that.