Why are cumulative tests typically weighted so high (U.S.)? Is there an academic justification behind most U.S. classes weighting exams at very high percentages of the overall grade in a course? So if a student does exceedingly well throughout the course in all projects, but bombs both tests, their grade is drastically skewed towards the exams rather than the coursework leading up to the exams.

Full disclosure, this happened to me this semester. I have a 97.75% on our projects throughout the course (4 major projects, each taking ~20 hours to complete). However, I admittedly bombed the final and did fairly poorly on the midterm (37% and 70%, respectively). Projects in our course are weighted 60%, but the remaining 40% is entirely midterm/final. My final grade for the class is hovering around 80% before the curve.

I want to understand the mindset behind these weights though, and where the idea of heavy cumulative exam weights came from? In other words, if I've demonstrated the understanding of the material to almost perfect standards, but I failed to represent that on a test, how does that translate to me being given a grade that doesn't really represent a strong understanding in the subject?
Cumulative tests show that you understand everything so far; they are meant to help students who perform poorly on the first exam, so they can do better on the second one, since they will have an idea of what to expect on the second one. It is uncommon when a student does worse from one test to the next.

Also, going back to projects, some professors don't value homework/projects as much because any student can copy / get help for their projects. Some professors I know would even give 100% for homework/projects just for turning them in, as they are meant for students to practice and learn by themselves. They are meant to help students prepare for tests. Because of this projects and homework are not a good (trusted) indicator of how a student is doing in a class.

By the looks on your grades, most likely you still don't know the topics of your class, if it was a more strict professor / class, just for failing the cumulative final, you would have failed the class as well, as this would be an indicator that you (maybe) cheated on your projects.

Cumulative tests are usually weighted high because in order to do the last topic you need to know the previous topics as well.