Just starting in grad school, I haven't heard from my advisor in three weeks … I just started grad school this year. I met with my advisor over three weeks ago, on the first week of school. We talked about the school, she told me a bit about the department and showed me around the office. She also talked to me a bit about putting together an advisory committee, but that's it. It lasted an hour, but we didn't really talk about my research project. She told me to get settled into grad school over the next couple weeks. She did recommend I watch some videos to help me get more familiar on the nature of the project, which I did.

I'm worried I haven't heard from her in so long. She's someone who likes to set up weekly meetings for her students, too. And now I'm worried to email her because she may have been expecting an email like two weeks ago. What do I do? Should I email her? What should I say? I was thinking of mentioning to her that I watched the videos she recommended. I think I'm already making a bad impression in grad school.
It is very important to have frequent communication with your advisor, even if you think you have nothing new to say. And it is NEVER too late to email her. Just tell her the truth, just like you described above. Advisors want students who are honest and can make adjustments as needed. I am well aware of how awkward it can feel to meet with your advisor when you haven't accomplished everything you think you should have or when you think you're running behind schedule, but that's what weekly meetings with advisors are especially good for - evaluating what the next steps should be and how to change things around to get things done.