Learn English – How “frequent” or how “frequently”

It is grammatically correct. From Longman Dictionary, "Over the years we’ve grown very fond of each other". In this sentence structure, the word "Fond" is an adjective. Grown acts like be. I have grown (been) fond of Alec. Gradual connotes a gradual process of fondness.

You can use the word grow plus an adjective, which means become. I have grown (increasingly) annoyed/satisfied. The sound was growing louder.

According to the Oxford Dictionary (meaning 1.3), we use a continuous tense with always when we want to talk about something that happens repeatedly and annoyingly.

Compare that with using always in the present simple (meaning 1.1) - at all times; on all occasions

I am always ready - At all times
I am always nervous when I have to speak before a large group of people - on all occasions

frequently is defined as regularly; habitually; often: we use it to talk about a number of separate instances that happen at regular intervals, and is only ever used with the a simple tense- as if we are talking about each instance separately.