As traffic grows, so will resource usage.
One way to reduce usage is to implement caching so that each page load doesn't hit the database. There are a number of caching plugins available, though WP Super Cache and W3 Total Cache are probably the most popular.
WP Super Cache is a bit easier to setup and works with very little configuration. On the other hand, if you need something more advanced and you plan on using Redis or Memcached to cache (instead of using the disk), W3 Total Cache would be a better, but more complex option.
Personally, I much prefer simple caching using Redis, though it's a bit more of a manual setup than it would be with the two plugins above. This is a rather simple plugin, but you'll need to install Redis, and then do some configuration in
wp-config.php to get it working as expected.
Caching alone, however, isn't a magic fix-all. Last I recall, the configuration for MySQL and PHP that ServerPilot uses is either the defaults or pretty close to it, so it's most likely not tuned for higher than average traffic (and by average, I mean very low to low).
Caching works as another layer to improve performance, but you also need to work on tweaking and tuning the stack itself (NGINX/Apache, MySQL, PHP-FPM, etc) to get the most out of what you've got.
Upgrading to a higher plan with more CPU might help, though ultimately, with the same configuration and no caching, you'd likely end up as you are now with higher CPU usage due to so much needing to be processed.