Do free TLD's affect SEO?

Country code top-level domains (ccTLD's) such as .tk (Tokelau, New Zealand) and .ga (Gabon) have extra weight in their own country's search engine (like google.tk and google.ga for instance) but that is as far as it goes.

That being said however, some ccTLD are considered gTLD (generic) by Google, .tk being one of them as can be seen under the 'More about domain determination' section here (thanks to Stephen in the comments). ccTLD's are an extra signal for Google to perceive the site as likely being more relevant to users in those regions/countries.

Google's John Mueller said this on the matter just in July 2015.

Q: What about real ccTLDs (country code top-level domains) : will Google favour ccTLDs (like .uk, .ae, etc.) as a local domain for people searching in those countries?

A: By default, most ccTLDs (with exceptions) result in Google using these to geotarget the website; it tells us that the website is probably more relevant in the appropriate country. Again, see our help centre for more information on multi-regional and multilingual sites.