Jughead doesn't want to worry you, you already have enough problems, just like him. Your problems are his problems, but he doesn't want his problems to be yours too.
Since he joined the Serpents, he has acquired not only problems, but also injuries. Which he hides from you. He arrived at the trailer with a bruised face today. He was just going to lay in bed and sleep, but you were there, with a big bag of burgers from Pop’s.
When you saw his condition, you ran to get the first aid kit.
"Come on, I'm fine." Jughead took his hands out of the first aid kit and hugged you. "It was just a stupid fight between the Serpents and the Cannibals." He sighed stroking your hair "I'm fine." He kissed her forehead "How was your day?"
He loved you very much. And put a lot into it. You were everything to him. His favorite person. And he would do anything for you. Anything.