Adding any extra elements to a site will naturally slow it down - every image, script, and font takes a certain amount of time to download and execute or render in the browser.
The collector itself is just 12kb and loads in less than 150ms on most normal broadband connections. It's then cached by the end user's browser and retrieved from the cache on subsequent page loads with no network overhead.
Each page view or click sends a data payload back to Prodlytic - this is typically less than 700 bytes of data and is transmitted asynchronously without affecting the page performance at all.
Overall we're confident you won't notice any perceptible speed difference after installing Prodlytic.