Your college education will greatly increase your income. This increases the government's tax revenue significantly, which is important. That education is an investment that will pay both you and the government back many, many, many times over during your life.
If the scholarship is coming from the institution itself, you're in luck because that makes the ethical considerations easier. They will simply write off some of the expense of teaching you. This is not the same as them giving you a pile of money. However, even if it was, there's a good case for why it still doesn't matter.
Suppose the institution is publicly funded. It gets money from the state's tax revenues. They give you a helping hand. Your education nets you far more money than someone who only has a high school diploma. That income is taxed. Education is a huge part of the budget in any state; my own (California) spent over $50 billion on it yearly the last time I checked. If you make more and get taxed more, a big chunk of that is going to go into helping other students. In a public institution, the government already foots almost all of the bill. Whatever you pay per term is a small portion of what the institution actually gets!
Furthermore, the government is going to gank your money year after year and spend it on incredibly stupid, unethical, wasteful things whether you agree or not. If they give you back 0.5% of what they take out of you, TAKE IT!!!
Now, suppose the institution is privately funded. It gets money from other students' tuitions, donations from living alumni, endowments from dead millionaire/billionaire alumni, and a few other sources like trademarks, patents, property holdings, etc. In the case of fellow students, they had the same opportunity to win that scholarship on merit, and did not; so if they don't get the scholarship, is it your fault? Hardly.
Likewise, suppose a dead billionaire bequests $50 million to the university. A great deal of that money is there solely because of the reputation and connections that billionaire enjoyed. You probably know that most of the reason people try to get into Ivy League schools is the gravitas of the university's name, and the connections that can be made there!!! Merely saying "I went to UCLA" or "I went to Harvard" will open doors that would remained closed if you'd said "I went to Bumf*** College of East Nowhere". If a tiny drop in that billionaire's bucket propels you to great success, increasing the glory of the university the billionaire loved to the tune of $50 million, I would see that as a positive rather than a negative.
Ultimately, it's up to you. These are all just rationalizations. Someone else will have different rationalizations. Some may say it's immoral, but morals are just opinions we automatically absorb from the people who we grow up around and go through adulthood with. Morals are almost never thought through; they are merely parroted for the sake of group membership, which is why the subconscious mind cares about them in the first place.
Instead, it's best to consider one's moral sense as a source of information, but hardly an infallible one. Consider morals in 1850 vs. today - is someone's moral conviction enough reason to think they're right? Certainly not! With ethics, the question becomes this:
"What are other peoples' rights and reasonable expectations?"
If someone says they have a reasonable expectation and/or a right to get the scholarship because they're poorer than you, ask why their interpretation is necessarily the only valid one. (I've given you plenty of valid interpretations above that are perfectly valid, so this is not difficult.)