Does GCM improve the strenght of weak passwords?
No, it doesn't make weak passwords magically stronger.  If they know part of the file (e.g. the header), or even is just able to recognize it, what they can do is, for each plausible password, just decrypt that small area of the file (and ignore everything else), and see if the decryption of that area is plausible.  Once the password guess passes that check, they can then do a full decryption and see if everything checks out.

To make brute forcing a weak password more difficult, I would suggest a strong (expensive) password hashing method, such as Argon2.

BTW: the estimated time of 1 msec to decrypt a 1kbyte GCM-encrypted file is far too large; I would expect that an adversary might be able to do it in perhaps within a few microseconds...