PT Watching the PT for the first time (otherwise very familiar with OT)

Oh man, you're making me tear up. For real. I guess I'm just as hopeless as you are
I know what you mean, and sometimes those "random unexpected tearjerking moments" hit only on subsequent viewings.

My interpretation is that while the Sith may have "arts" of their own, much Sithliness is just "negative" in the sense of Jedi-ish Force skillzzz + emotional fuel; ie you don't have to positively know any philosophy or special Sith powers to count as a Sith. This may be at odds with the EU's distinction between Sith and "Dark Jedi/Force-sensitives" more generally, but that's a distinction the movies don't draw, so I disregard it.

I think Obi-Wan just really doesn't like schmoozing with Senators and their hangers-on -- politicians remind him too much of himself
Seriously now, I think he just wants to give Anakin some privacy for his reunion with Padmé. It does say in the opening crawl that they've come straight to the battle from the Outer Rim sieges, so we can infer that they've been away from Coruscant for quite a while. He knows that as a leading member of the Senate, Padmé will probably be there to meet the Chancellor. He definitely knows Anakin and Padmé have a thang going on, and probably knows that Anakin thinks he doesn't know. So he just hangs back quietly and lets the kids have their fun.

It came across as tragic to me. I think it was at that moment that I sensed with certainty that she would die before the film ended. (When was it for you?)
He's certainly possessive, but I think he really did love her, as much as that "love" was mixed with and screwed up by his hang-ups about power/control, his insecurities about not being good enough for her, etc. And that particular line came across as being more awestruck/insecure than territorial, to me. I hear little Ani in it.