My idea is that the effects already
were massive (potentially, or not, depending on how one takes it). We live in the world that was already changed by the time traveler.
The question is, what event did the time traveler successfully stop, and how successful was the stoppage of that event at altering the perceived repercussions of that event. It could be that the same basic events still happened in our new history as they did in the original history, just shifted around a bit. For example, maybe the meteor originally wiped out some city like Berlin, and Russia sensed weakness and attacked Germany, and that was the start of World War I (rather than the assassination of Archduke Ferdinand). Or something. In the changed history, the same basic events ended up happening, if delayed a couple years, because they had been building for a long time and no one event, even something as large as a meteor, would alter the outcome significantly.
Or one could take the other tack—the meteor did something very bad, but the changed history ended up worse.
Anyway I am not near enough a student of history to think this through thoroughly, and don't want to become enough of one. That's why I'm not going to attempt to write a story like this.