Hello. I'm just curious, what are some countries that many ordinary Koreans have much interest in? Do many Koreans have interest in the countries that are economically much weaker than Korea?

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South Korea is a small divided country and it's far from a 'powerful' country in my opinion. Many Koreans me included don't think that Korea is a 'rich' country. There is no reason for Koreans to not have interest in "weak" countries.
In my opinion, compared to the people from many other countries, Korean students are taught quite well about other countries in the world in school. I'm 40, but I still clearly remember every single capital city and national flag of other countries that I memorized when I was an elementary school student.
So, other than some seriously ignorant people, many Koreans are generally very good at world geography and they know many things about other countries. We're also very interested in all kinds of worldwide issues and enjoy talking about them. Also, we love to learn about other countries and often travel abroad to experience different cultures.

I'm interested in all countries in the world. But if I had to choose some of them, I'd say, Bhutan, Brunei, India, Iran, Iraq, Belarus, Moldova, Belize, many African countries because (other than India and Brunei) it's not that common for average Koreans to go to these countries for sightseeing. It's also because I've always been interested in the Mesopotamian civilization (Iraq) and the Persian civilization (Iran).