Since you're accepting nice criticism, here I go writing an essay once more:
Writing Quality: 5 stars. There are hardly any errors in sentences, making it good and very fluent to read. Sentences are smooth, paragraphs are spaced out properly, making it neat and easy on the eyes. The chapters are also of appropriate length (if I estimate properly, it should be around 1.5k words? Correct me if I'm wrong), and if this quality is maintained, it could be considered a "good" fanfic just based on writing quality.
Stability of Updates: It's only 7 chapters, so I can't really judge based on that. So it's a mere 4 stars since author said weekly for now. It's not the best, but not the worst either.
Story development: Once again, it's only 7 chapters, so I can't judge much. But based on what happens in 7 chapters, I can roughly guess the plot of which you are trying to bring across. It's nothing special, with some sort of passive-aggressive "revenge" (if you can even call it that) for his adopted grandfather's injuries. Unless you bring across more surprise other than just revenge, this would probably remain at 4 stars. These four stars also assume that you can properly weave in the MC's personal problems with the plot smoothly, and you're not just separating the two like oil and water. Otherwise, this drops to 3 stars. However, if you manage to weave in your own (unique) plot along and with your MC's problem, and not just follow canon, this can go up to 4.5 - 5 stars.
Character design: So far, it feels rather bland. I mean, his personality is indifferent, from what I see (others may find different), and while that gives off the cool, silent type vibe, it doesn't give a lot of "feel" to the characters. Why do you think most Shounen actions manga/anime has a hot-blooded MC? It's because it gives off a lot more "life" to the story. The silent/cool MC usually remains as the side character.
I'm not saying that it is bad or anything, but it's just a lot harder to develop a cool mc, and if you're the first-timer you said you are, you might find a problem trying to find a good development for your mc, whether in his thoughts or behaviors. Most of the other characters are also not really talked about, which is understandable since it's just mostly canon events, but I hope in the future that you will properly develop them. It doesn't matter whether or not your readers know about them beforehand, it still does some good (mainly for you, though) to get to know them personally when writing them rather than just reading from a manga. It will also help you develop more types of personalities you could write if you're planning to write even more books after this. Therefore, this is also four stars for now.
World Background: This is fanfiction; most of the background have already been properly developed by their original authors. So automatically 5 stars.
But if you're asking for how well you have developed the world background, I would give it a 4. You didn't give the world background all at once, which is a good thing. The clues that you drop here and there acts as good appetizers for your readers to continue reading on. However, it's really too sparse. If I didn't know MHA when I read this, I would be curious, but I would be equally lost until you finally develop it properly.
Conclusion: In the end, this isn't really a criticism, so to speak. Generally speaking, this story definitely has potential when developed properly. To be completely honest, my writing style is completely opposite from yours. While yours tend to drop clues here and there as you immediately get on with the main cast, I develop mine very slowly, starting from childhood, to middle school, to finally high school. I have tried writing an MHA fanfic as well, and while I have a lot of supporters, I know that I could do a lot better.
So here is a tip for you - go and read other mha fanfictions for ideas and development. THE TRIALS: Path Toward Godhood is a good one that I really love, so you can go ahead and give it a shot as well.
4.4 stars is a rather average rating that I would give. But then again, it's only 7 chapters so far. The future is for you to create. Perhaps I will come back and review once more chapters have been published,
