Not sure if they know the weight, but they usually just measure your tummy to get an idea of the size. Not sure about the rate of growth in the last tri, but i seemed to just go bezerk in size in the last 4 weeks. Alot of that was fluid too. I looked quite big as i am short!!!LOL . I think i was as wide as i was tall in the end. All good though, its so gradual, and you will cope just fine.
Yes, i do believe i was getting extra CM later in the preg about the third tri. I think some people even get it a bit earlier.
All the best.