So I got the inspiration for this headcanon from the wonderful hpaddict_marauders and her book Make it Through the Night. Go read it if you haven't already, it's fucking awesome!
Arthur Weasley 100% for sure had countless pictures of his family in his wallet. Like a whole ass photo album hidden in there and whenever he saw people he'd show them the pictures while gushing over his family.
"Oh hey, long time no see! LOOK AT THESE PICTURES! THAT'S MY ELDEST, BILL, AND THAT'S GINNY, AND THAT'S PERCY AND MOLLY AND FRED AND GEORGE AND RON AND CHARLIE AND OMG I LOVE THEM SO MUCH THEY MEAN SO MUCH TO ME THEY ARE THE WHOLE WORLD I'D DIE FOR THEM LOOK AT THEM ADMIRE THEM NOW."
Don't tell me James didn't do the same thing.
"Hey, Sirius! Look! IT'S HARRY! AND LILY! AND THEY'RE SO AMAZING AND THEIR EYES ARE SO PRETTY AND LOOK! HERE'S ANOTHER PICTURE FROM HARRY'S BIRTHDAY! THEY'RE BOTH EATING CAKE AREN'T THEY SO CUTE I LOVE THEM MORE THAN I LOVE QUIDDITCH AND MCGONAGALL AND I'D DO ANYTHING FOR THEM LOOK AT THE PICTURES THEY'RE SO BEAUTIFUL I'M GOING TO CRY."
Yet nobody could ever find Arthur or James to be annoying because they're just too damn precious and too pure for this world.