Looking on the internet deeply has found these results:

I will be grateful is the most popular phrase on the web.

I will be very grateful 1362,000 results on the web	I will be grateful 121,400,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Miss Lane will be very grateful. I feel that the interpreters will be very grateful, as I am, because I will be able to recognise German spoken by a Spaniard more easily next time. I am very grateful for your offer, Mr Barroso, and I will be happy to take you up on it. I am very grateful to Parliament. I am very grateful for this flexibility. I'm sure General Franco is very grateful. There is a lot of work to be done and I will be very grateful for your support in developing this policy area. We are very grateful for the advice and I hope my colleagues and I will be able to remedy that in the forthcoming general election.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

I will be very grateful

1362,000 results on the web

I will be grateful

121,400,000 results on the web

More popular!

Miss Lane will be very grateful.
I feel that the interpreters will be very grateful, as I am, because I will be able to recognise German spoken by a Spaniard more easily next time.
I am very grateful for your offer, Mr Barroso, and I will be happy to take you up on it.
I am very grateful to Parliament.
I am very grateful for this flexibility.
I'm sure General Franco is very grateful.
There is a lot of work to be done and I will be very grateful for your support in developing this policy area.
We are very grateful for the advice and I hope my colleagues and I will be able to remedy that in the forthcoming general election.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.