He’s a caretaker of Holmes, a bridge between reality and Sherlock’s head. Of course, a medical doctor would indeed always evaluate the state of their patient (even when he’s a friend). Does Watson go beyond a professional involvement, though? He can’t seem to stop saving Holmes.
Tidy, brave, prepared — Sherlock himself names these traits for Watson. He’s also courteous. When Holmes insults his fiancee, Watson restrains himself in a public restaurant with a lady. He approves of her wine toss in Sherlock’s face, and he later, when alone with him, punches Holmes in the nose. This Watson has a physicality controlled by good manners.
The two of them are like an old married couple, sniping and circling, knowing everything the other is thinking. Holmes is so erratic (these days we would say he’s on-spectrum) that Watson initially seems grounded and normal.
He’s not, though! His co-dependency with Holmes is possible because they’re both strange men. Watson is just better at socially hiding it. What would he do if he couldn’t roll his eyes at Holmes? He’s able to pretend he’s a regular bloke by showing exasperation with Sherlock. This isn’t the traditional sidekick role. Law’s Watson is an actual character with separate motivations.
He’s a Nine. The competitive spirit between him and RDJ’s Holmes, a Seven, is appropriate for these numbers. And Watson is very much someone who thinks as a Body Type. He enjoys the intellectual pursuit with Sherlock, but he prefers his profession — tending to the physical — and clues that require him to interact with them. He is a Nine who pushes the edges of his Enneagram: a little bit daring and reckless, a little bit angry and injudicious. He hates himself for it, but luckily he can blame it all on Holmes.