I would expect "I'm from Earth" to get about as much respect as "I'm from Olduvai Gorge". Well, isn't that nice for you, basically, but that's it. It's not a hard guess, we already don't reward people just because they were born near the origin of humanity.
It'll be a while, though. There will certainly still be a long period of time where Earth is the most powerful by sheer inertia, no matter how fast space civilization develops.
> I would expect "I'm from Earth" to get about as much respect as "I'm from Olduvai Gorge".
Maybe that's because we don't have cultural traditions that identifiably connect us to that. (We probably do, but they're so deeply ingrained that we can't even identify them as "culture").
People of Italian extraction have a certain affinity for Italians, German-descendants for Germans, etc- Unless we just totally forget about Earth-That-Was I think it's reasonable to think we'd find it interesting in 1000 years.
How much interesting stuff is there to learn about Olduvai Gorge though?
I expect Earth will be viewed as we view Athens now. There's a lot of important history which happened there, and schoolchildren spend a lot of time studying it, but the center of the action has moved elsewhere.
Instead of "How often do men think about ancient Rome?", people will ask: "How often do men think about ancient Earth?"