Ask a simple question, get a simple answer: yes, Google certainly treats the Big Three differently than it does .co or .ly. I don't have specific evidence of them discriminating against .co/.ly, but the evidence that they discriminate for EMDs in the Big Three is overwhelming and undeniable.

Is this not a bias? As in: It only looks like Google discriminates for the Big Three, because they are so abundant?

I've heard from official sources like below that Google doesn't discriminate on TLD. There are my sites and Googlers who use ".info" TLD in a legit and well-ranking manner.

Where this "evidence" does play a role, is in spam/made for Adwords-sites. It is reasonable to assume that a .co or .ly will get more attention, to combat spam/made for Adwords sites that try to use Keyword-In-Domain tricks to outrank legit companies.

But if you are not making Keyword-In-Domain Made-For-Adwords sites, you have nothing to worry about (at least as for Google discrimination).

It is mostly _users_ who discriminate for a .com. If Google ranks website.ly in the top 5, but its users don't click on the result, in fear of spam or low-quality, then your rankings might suffer.

Matt Cutts interview on DomainRoundtable.

  "For example, do .com domains carry more weight than a 
  .net, .us, .info, etc. 

  He said that TLD doesn’t matter -- that’s the way Larry 
  and Sergey originally designed the Google algorithm. The 
  algorithm doesn’t care where the page is located, it’s 
  all about pagerank (LINKS) of the particular page. At the 
  end of answering this question he did admit that they 
  might have started to look at particularly cheap (and 
  spammy) TLDs differently than other TLDs or they might 
  start considering TLD in their algorithm if they’re not 
  already doing so."

So it is still good to advice against .io and witty domain names (portfol.io), but not for the reason of Google discrimination.

I am reminded by statements like: "For better ranking, claim your domain for 5+ years". Just because Google gives extra attention to domains with a low expiration date, because they correlate with spammy/get-rich-quick sites, doesn't mean that spam on a 5+ years registered domain is ok, or that simply claiming a domain for 10 years, somehow signals quality to Google.

You only have to worry about registration dates, when you know that you deliver low-quality content and you don't want to be found out soon.

Does Google still give weight to the .edu domain? It'd surely be unhelpful to proper meritorious rankings seeing as it's one of the first strategies SEOers will use?

What percentage of Mexican men perform oral sex on their wives

oh yes. they do. just check in google webmaster tools the respective setting and help files. there're just dozens of TLDs which rank internationally incl. the blockbuster .com .org and .net. first we had the fancy .io domain but switched quickly to a .com -- traffic has been exploding since then

yes - some TLD's are known spam havens. see co.cc, for example.