Specifically for Google, if you use two-factor authentication it is safe to "weaken" your password "from a 16-character password with a search space on the order of 1030 to an 8-character password with a search space on the order of 1014" as long as you use a good 8-character password (i.e. completely random and not re-used across sites).
The strength of two-factor authentication lies in the assumption that the two factors require different kinds of attack and it is unlikely that a single attacker would perform both kinds of attacks on a single target. To answer your question we need to analyze what attacks are possible on weaker passwords compared to stronger passwords and how likely it is that someone who is able to attack weaker passwords but not longer passwords will attack the second authentication factor.
Now the security delta between "a 16-character password with a search space on the order of 1030" and "an 8-character password with a search space on the order of 1014" isn't as large as you may think - there aren't that many attacks that the weaker password is susceptible to but the stronger one isn't. Re-using passwords is dangerous regardless of the password length. The same is true for MITM, key loggers and most other common attacks on passwords.
The kind of attacks in which the password length is meaningful are dictionary attacks - i.e. attacks in which the attacker does an exhaustive search for your password in a dictionary. Trying all possible passwords in the login screen is obviously not feasible for a search space of 1014, but if an attacker obtains a hash of your password then it may be feasible to check this hash for a search space of 1014 but not for a search space of 1030.
Here is where the fact that you've specified Google in your question is important. Google are serious about password security and do what it takes to keep your hashed passwords secure. This includes protecting the servers on which the hashed passwords reside and using salt, pepper and key stretching to thwart a hacker who has somehow managed to get the hashed passwords.
If an attacker has succeeded in circumventing all the above, i.e. is able to obtain Google's database of salts and hashed passwords and is able to obtain the secret pepper and is able to do an exhaustive search with key stretching on a search space of 1014, then unless you're the director of the CIA that attacker won't be wasting any time on hacking your phone to bypass the second authentication factor - they will be too busy hacking the hundreds of millions of Gmail accounts that don't use two-factor authentication. Such a hacker isn't someone targeting you specifically - it's someone targeting the whole world.
If your data is so valuable that such a powerful hacker would target you specifically then you really shouldn't be putting your data in Gmail in the first place. For that matter you shouldn't be putting it on any computer that is connected to the Internet.