Trying to resize baby hat pattern-help!

[Kimbatigger]

I have a directions for a newborn hat, which I have made with size four needles and baby sport yarn weight 3 as directed. The hat pattern is too small for babies 3-6 months old, but I want to use the same pattern. I have some Baby Amore yarn weight 4, which recommends size 8 needles. The problem is that the same pattern with this yarn and the size 8's makes the hat way way too big (it fit me). Can I use the weight 4 yarn with the 4 needles to increase the size? What is the best way to do this? I really like the baby amore yarn and want to use it. Thank you for any help.
Regards,
Kimbatigger