Here's how you could use it:
* "The weeds in my garden grow obstinately, despite all my attempts to remove them." (Implies the weeds are persistent and difficult to eradicate)
* "Her hatred for him grew obstinately, fueled by his betrayal." (Implies the hatred is strong and doesn't lessen over time)
The key is that "grows obstinately" implies a process of increasing in size or intensity despite obstacles or attempts to stop it.
It's worth noting that "obstinately" is a strong word and carries a negative connotation. It suggests something that is unwilling to change or be controlled.