If you reuse your pad, you're vulnerable to frequency analysis, which is literally the oldest trick in the book. You might as well send in plaintext.

How easy would it be if you would go through the entire 1GB and only then from the beginning? I guess it is a question of how big messages are.

If you're only reusing it once, then I guess frequency analysis gets tricky, but the problem you have instead is that you have provided a validation function: Where, using a one-time-pad, any key that yields plausible cleartext is a possible candidate, if you have two cyphertexts encoded with the same (piece of) the one-time-pad, only keys that result in plausible decrypted cleartext for both cyphertexts are possible candidates.

This was how an early break-through in breaking the Enigma was achieved (tangentially, as the Enigma isn't a one-time-pad, but the analysis is similar): Codes were rotated daily, but the first message sent out every morning with the new codes was a weather-report. Thus, the team could immediately cull the search-space to keys that would decrypt to "Weather on [date]" for the first n characters.