Hi soyebmandal,
From what I understand, you have two problems here:
Firstly, your database is too large - taking up more disk space than your host would like.
Secondly, your website is transferring too much data from the database to be used by the site.
I'm a database developer with over 10 years experience working for the UK's largest retail banking group. I have completed numerous projects, building and refining database applications for customers who need to keep their costs down.
To resolve the first problem, I would ensure that your database is as normalised as possible.
This means removing duplicated information by storing it separately and using database relationships so that all information is still available to your website.
To resolve the second problem, I would rebuild your SQL queries. The chances are that they use "Select * From" fairly often, and this needs to be changed to only load the information that's required.
To ensure that you're happy with my solution, I would have a look at your database and provide you with a plan of the work I would do.
Please feel free to ask any questions you may have. I'm not the cheapest option in your list of candidates, but I have a lot of experience and will get the job done for you.
Kind regards,
Ben