Incredibly weak is correct and even bordering on understatement. They are below the noise floor by about 50dB (which is a logarithmic scale, so is a factor of 100,000x).
It still blows my mind that gps even works given how far below the noise floor it is. I am very far from being any sort of expert in radio theory but my layman understanding is that the receiver "knows" exactly what a gps signal should look like and somehow magically uses that to extract the data out of the noise. It is one of those absolutely genius aspects of modern life, and we tend to just take for granted
Same. I am pretty comfortable as a programmer and that translates to feeling moderately comfortable at gluing together blocks of digital electronics. Analog electronics are much more of a struggle and RF is entirely black magic. The idea that GPS works at all defies my understanding of what ought to be possible.