What's the purpose of this checkerboard pattern?
That's called copper thieving.  It helps balance the amount of copper on the outer layers which makes the etching process easier.  Basically it helps them avoid over or under etching the board.

Usually I'll have a note on my board files that I send to the fab house like: Fab may add copper thieving at their discretion so long as it is at least 100 mil from any major feature.  Which basically means theive all you want but don't get it near any of my signals.

Why not just fill the outer layers with copper pour then?  It's not cost, etching a pcb is not an additive process.  They start with a full sheet of copper and burn it away. Having copper pour all over the place close to my signals!!! That would cause impedance discontinuities everywhere.  

Plus depending on how it's routed you don't want to unbalance your board, for example having plenty of copper pour on the bottom but little on the top.  That will lead you into having your board cup and curl when it goes through the oven.