Do Drupal websites have bad performance or are heavy?
What's your hosts memory limit?

For MySQL Run this MySQL command

SHOW VARIABLES LIKE 'innodb_buffer_pool_size'


If it's at the default I would see if you can increase it to at least the same size as your database. If you can not, I would look at converting some of your tables to MyISAM.
http://www.mysqlperformanceblog.com/2007/11/03/choosing-innodb_buffer_pool_size/