im currently weighting my attributes but is there an extension or a company out there that is known for improving the search in Magento 2 specifically.
Sphinx was always the preferred search technology for Magento 1 and same goes for Magento 2. You can check this extension from mageworx: http://www.mageworx.com/magento-2-search-extension.html
We also use cloud search services in another shopping cart we support with great results but do not have one setup for Magento 2 yet - it works instantly and does not take resources from your main server because it runs at search provider's servers. You can check this one: https://marketplace.magento.com/instantsearch-instantsearchplus.html
note: those services have monthly fees but they worth the expense, especially if you run a very active store where search can put a extra heavy load on your server.
Hope this helps.
You can try this extension https://marketplace.magento.com/amasty-xsearch.html
With this extension you can: