Creating an incremental database copy in PostgreSQL
There isn't really anything like this.

You can use pg_basebackup or pg_dump to copy the original DB, but there's no copy-on-write facility. The built-in replication requires a shared-nothing copy and the replicas are read-only.

You can use 3rd party replication options like Londiste or Slony-I to replicate the state of the master to the dev machines, but these systems are a bit fragile, don't deal with DDL replication, and can have a significant impact the master server's performance.

Future PostgreSQL versions will hopefully have log-streaming logical replication which would be closer to what you want. It exists as a patch to the source code now, but at time of writing (Pg 9.3 release) it's in alpha stage development where it's validated for a couple of uses but not for general use.

I'd probably go a layer or two down. I'd use file-system copy-on-write snapshots, or even copy-on-write virtual machine images, to achieve what you want.