Magento 1

In Magento 1, use this module: Catalog > Manage attributes
Every attribute that has the Use in Quick Search setting set to Yes and/or has the setting Use in Layered Navigation set to Filterable will automatically be sent to the Tweakwise app:

And/or:

For attributes of the Text type can't set the Use in Layered Navigation setting to Filterable. In that case, setting the Use in Quick Search setting to Yes is sufficient. The export needs to be regenerated to apply the setting to the Tweakwise app.

Magento 2

In Magento 2, you can manage this in the module Stores> Attributes > Product
You can set whether an attribute will be sent to the Tweakwise app in the feed in the module Storefront Properties. 

When one of the following settings is on, the attributes will be exported:

• Used in Layered navigation
• Used in search results layered navigation
• Use in search
• Visible in advanced search
• Used for product listing 
• Used for sorting in product listing

The export needs to be regenerated to apply the setting to the Tweakwise app.