This is actually very normal. When my eldest daughter hit 6 or 7 years old, her anxiety levels seemed to increase and things that didn't worry her before suddenly did. My now-7 year old has had this same anxiety now for about a year and I've talked to our pediatric neurologist (that we have for my other two daughters) and our pediatrician and both say that it's completely developmentally normal.
The difference is that when they hit 6 or 7 years old, their world suddenly becomes a little bit bigger. They realize that other people really do have feelings too. They realize that other people's feelings are important. They notice that the world isn't all rainbows and unicorns and not everything is not only not in their control, but not in Mommy and Daddy's control. And that some of those things are Bad Things.
I take a very different tact than you do. I DO reassure my daughters. They NEED that reassurance. I have the discussions and follow through with them because they ask, "Well what if you're wrong?" and we discuss that too. My response is, "Of course the bad thing you're worried about COULD happen but it's much more likely that the good stuff will keep happening. Here's how I know that: EXAMPLES/REASONS"
It's also fine for my kids to see me cry. They need to know that Mommy isn't always happy and joyful, and they need to be able to see me work through emotions. It helps teach them to work through THEIR emotions too. If your daughter sees you cry, and sees your crying as therapeutic rather than something horrible that twists up her stomach as anxiety inducing, it would be much better for her. Then when SHE cries, she'll see that crying can be a positive thing and she'll be able to work through HER anxiety better.
So far, my eldest's anxiety is very much intertwined with her ADHD and it always has been. She's ODD and argumentative, and she talks, talks, talks and is a huge ball of nervous energy. She's moves around nonstop. That's now she works out her anxiety.
My youngest is the worst with the anxiety, but she talks to me. She helps me with chores. She draws. We work it through.
My middle daughter... well... her anxieties are all tangled up in her special needs and bubble out at different times. That's for another post.