When my first grandson was born 10 weeks early I wanted a hat that would grow with him. At 30 weeks (when he was born), he wore it with a brim, but by 36 weeks it fitted perfectly.
Should fit a preemie / small newborn from 3lb7 to 6lb.
Can be sized up easily by using larger yarn/needles. e.g. Sirdar Click Chunky with Wool on 4.5mm needles.