Why are some of my beetroot plants coming up?

Doesn't sound abnormal to me. Sometimes birds try to pull them out, like onion sets. But we've had perfectly good multi-seeded beetroot growing right above the soil with only thin roots going down, which have still produced a good beet. I wouldn't worry about it as long as they are still rooted into the soil.

My beetroots always swell up above the soil level. I assume they are keen to be eaten!! You can earth them up a little if you want to.