The @verified badge does not really signify a "big enough" name. Back when it was a manual process, unless you were a huge celebrity, you got on the list if you were a member of a media organization and if Twitter happened to contact your comms/social media person to submit a list of employees and Twitter names. People with just a hundred or so followers could be verified this way.

Now that you can apply to be verified, just about anyone can get the blue checkmark. You just have to provide proof of identity and fill out a form. I didn't get verified through the manual process even though I worked at a fairly prominent media org. But working in non-media, I got accepted within a couple days by filling out the form.

Check out @Verified's following-list and you'll see lots of similarly non-influential people on there: https://twitter.com/verified/following