I have one of these interesting devices, mentioned on my
old website. Mine is rebadged as Wega CW-M1 For Video 3 - no mention of Sony. It's certainly great fun to watch.
The BetaStack AG-7 or CW-M1 came with a special plastic bracket to attach it to the C7 VCR. First you have to remove two screws from the top cover of the VCR, place the bracket over the holes and refit the screws to secure the bracket. The Betastack then clips on to the bracket. When not required, the Betastack can be unclipped and removed from the VCR, leaving the bracket behind. Of course, if the two items are separated and the VCR is disposed of, the bracket is lost. The brackets are consequently very rare.
You also need an external power supply, centre negative, it's either 6 or 9 volts DC. The bad news is I can't find either the bracket or the power supply for mine at the moment.
As for what they were used for, Sony marketed the C7 as an advanced VCR which it was in its day. One of the advanced features was a multi-event timer which could record daily or weekly TV programmes from different channels. With the Sony C7 and Betastack, you could go on a 2 week holiday without worrying about missing your favourite programmes, according to the marketing brochure. It didn't catch on though. VHS Long Play offered 8 hours recording on a single tape which was cheaper and easier. Nobody seemed to care about the lower quality. I think the Betastack was used in duplicating factories for a while, producing pre-recorded movie tapes.
Note the Betastack internally has many mechanical parts, in particular there are two nylon levers on either side which have a tendency to crack, causing it to stop working.