This isn't a phenomenon, this is compression. It is simply how it works.
Compression works by taking an input, runs it through some algorithms and then gets an output that matches up either exactly (lossless) or approximately (lossy) with the original input. It is not stored like normal video data as a set of pixels, but rather some form of data that models the original set of pixels using less space.
When you decode a video, it works from the compressed format and generates out a stream of pixel values that can be played back as actual video. When you transcode from one format to another, the video first goes through this decoding process to get a set of pixel color values and then goes through the encoding for the new format.
What you seem to be missing is that it does not matter how high quality the actual signal is that goes into the encoding, it will work off whatever you give it. You could save a low quality, artifact riddled, grainy, nasty, noisy video as a lossless format and you would end up with a perfectly preserved low quality, artifact riddled, grainy, nasty, noisy video. There would be no further degradation in quality, but you still have crappy video and it takes a huge amount of space because it is not storing an approximation of the crappy video, but rather the exact data.
If instead you were to use a lossy compression that was "similar" to the quality level of the video, you would introduce even more bad artifacts and lose any semblance of actual signal that was left in the video.
This principal is also referred to as generations of loss. It is mostly a carry over from the analog days when no copy was lossless and thus the numbers of generations of copies had to be kept to a minimum to preserve quality. With the digital era, this problem was greatly alleviated since a digital file can be copied perfectly, however it still lives on in transcoding where there is generations of loss.
This point actually also explains why the SD video files are so much larger than you expect. Most consumers are use to end-user compression formats with relatively small file sizes. These file sizes are great for end users because they don't need to be edited with or re-encoded, however such formats rapidly fall apart when you try to encode them again because of their small file size and large amount of loss (even if it isn't readily obvious to a normal viewer.)
Production quality DV video used a gigabyte or more of storage every 4.7 minutes or so, so it isn't at all unexpected that your high quality SD capture (even if the source itself was crap) is "large" by consumer standards. If you don't need to edit the videos, it is perfectly fine to transcode them as finished videos to a low bit-rate consumption file size. I'd recommend using 2 pass VBR encoding for this purpose, h.264 should do fine and you could use a low bitrate.
Bit rates are ultimately what determine file size in compression. The bit rate defines the amount of data that is allowed to be used to encode the video and roughly put, the compression algorithm will approximate the footage as best it can with the given bit-rate. The lower the bitrate, the smaller the file, but the lower the quality and the less able you will be to re-encode the video in the future without catastrophic quality loss.
As far as what levels you can use without noticeable quality loss for a final output, that really depends on the content and is far too broad for a Q/A site without a sample of video to look at. Compression is an incredibly complex field with lots of options and there are people who do nothing but handle doing compression for their entire living. The colors, the amount of motion, the amount of noise, etc, all have an impact on how much data is actually required to store the video in a way that the end user won't notice artifacts.