When both Martha and Marguerite said it'd be fine for him to stay, he was relieved. At least then he'd be there if Marguerite needed him. He and Marguerite were still having an adjustment period with each other. Given the lies and distance they'd had in their own world, it made sense. But at least now they could move forward together as a couple. That is what mattered most to Percy. Well, right behind Marguerite recovering from this illness.
It was a frightening diagnosis, but Martha's reassurances were hopeful to Percy. He was more than glad that she knew what she was doing, and he hoped the medicine would work. Percy would contact Marguerite's director with the diagnosis and all of that so that he wasn't having to worry and would be able to know when to expect Marguerite back.
"Thank you, Martha." Percy said with a smile. Because manners said one always thanked those who helped them. So he would ensure Martha knew her efforts were appreciated. And Percy was also grateful that she would be able to give him something to hopefully stave off illness for himself. The last thing they all needed was him to fall ill the same time Marguerite did. That sight might not exactly be a pretty one.
When Martha was going to go get the medicine and beds made up, Percy moved over to Marguerite and took her hand in his own, squeezing it, giving her a gentle smile. He didn't say anything, he didn't really need to. The gesture said it all for him, that he would be there for her.