1: Switch hosts
For this much content, you need a more powerful server. A shared server is unlikely to hold up with this much information in the database, so you need to look into a VPN, dedicated server, or possibly even a load-balanced setup. That partly also depends on how much traffic you are getting or expect to get – the more people using the site, the more the database is accessed.
2: Optimize database
A few things you can do are: turn off revisions and autosaves (and delete the ones that are already save); use a db optimizing plugin; and remove some of your plugins. Some plugins save a lot more information to the database than others – spend some time looking through your tables and find out where there’s a lot of information stored, particularly if a plugin is saving a lot in wp_options. If you can remove or at least replace some of those plugins it will lighten the overall load on your database.
3: Cache everything
You should also experiment with various forms of caching, from plugins to server setup. This can help immensely by reducing the number of queries to the database.
4: Check your theme
Some themes are more data-intensive than others. Try a few different ones and also try a query optimization plugin to see what your theme (and plugins) are calling, and find ways to reduce the complexity and number of queries.