An eggy Q

My RIR has just started laying and I've noticed that each egg she lay's is slightly larger than the last. Her first egg's shell was almost white and each egg's shell since has been darker in colour is this what usually happens? at what point does the egg colour settle? I'm intrigued about. 

It's interesting isn't it?

Over the first few months of laying, my pullets' eggs gradually got bigger.  They've been laying for a few months now and although their egg size has settled to a certain extent, they are still gradually getting a bit bigger.  

Also my Light Sussex pullet went broody and stopped laying for a few weeks, and now she has started again with her pullet-sized mini eggs.  But this time the size is increasing much faster than it did originally.

My Barnevelders lay 65g - 70g eggs, the Barred Rocks lay 60 - 65g eggs, and the Light Sussex is now laying 55g eggs although they are increasing in size.

I think the pigmentation on an egg usually decreases over the laying season so I would expect them to get lighter rather than darker.  I can't explain your girl's darker eggs.