Influencing the U.S. gives you the best leverage on your dollars. The U.S., for better or (more probably) worse, is the leading country of the West. It has the largest population, the largest economy, the dominant culture, and, most importantly, the largest military.

This is also why Israel lobbies and exerts such outsized influence the USG.

Most probably because United States influences them so much.

As an Iranian, United States politics have brought so much misery upon my country, I feel like we should get a vote in U.S elections at this point. Or I don't know like half a vote. Or 1/10 of a vote. I don't know somehow let us be heard our country which once was on the path of reforms and whatnot is being crushed under the weight of senseless sanctions!

Disclaimer: Current U.S. resident, rant over!

The short answer, from an American perspective: we love influencing the rest of the world, so they'd like to return the favor.

Plus, this way you don't have to pay US income tax.

So they're trying to improve America as revenge?

I don't see a revenge motive. More like "I believe my country/business/whatever is unduly influenced by this superpower, so I'm going to influence the superpower directly."

As a Canadian this is a good description of why I make a fair number of comments about US politics on the internet. I'm not sure I'd call it unduly though, it's somewhat inevitable that superpowers influence foreign politics.

Because America influences the world we live in. When you live in the empire, keep one eye on Rome.

Because the US loves to meddle in the policy of foreign countries. That's reason enough for powerful people in other countries to try to do the same in the US.

TLDR; America rules the world’s financial system, and much more. So the world has good reason to be interested in American politics.

American senators run shakedowns on whole countries.

Americans love to think they 'influence the rest of the world'. The reality is that a powerful cabal of billionaire offshore oligarchs such as Hansjörg Wyss effectively manipulate planetary politics to their ends. Given Wyss's altitude it seems likely he is meddling in many other sovereign state's politics too

The null hypothesis is that both dominate the world's politics. No need to be picky.