When I was using marijuana heavily I had very bad anxiety, not when I was using, but when I was not using. I would get really sad and cry for no reason, it was debilitating. I also had intrusive thoughts and feelings of doom and the whole heart palpitation when going to sleep thing happened to me as well as some sort of recurring panic attack, or at least that's what I assume it is.
The strange sleep problems took a very long time to get better, but the excessive anxiety went away very quickly. Do I still have anxiety and intrusive thoughts? Yes, but is it as bad? Hell no, the difference is night and day.