Did a basic test where I stripped my companions (in this case ED-E and Arcade, though I did a similar test with Veronica with the same results) of all visible items before entering the Silver Rush. Once inside ED-E's carried weight drops from 1 to 0, Arcade's drops from 10 to 2. Then when I exit the building and the guard outside hands me my weapons back, ED-E's carried weight has gone to 2 instead of back to 1, and Arcade's has gone to (you guessed it) 18 instead of 10. So it seems pretty clear they're getting a duplicate of their hidden default weapons.
I was able to keep on doing it, increasing their default carried weight each time. 1, 2, 3, 4, 5, etc, and 10, 18, 26, 34, etc, for ED-E and Arcade respectively. Interestingly after their weapons are duplicated, only their duplicate weapons are taken on subsequent trips inside the Silver Rush. So Arcade will drop from, say, 26 to 10. But after exiting he'll get all the duplicates back, plus another duplicate.
It doesn't affect weapons I've given them to use/carry, so far as I can tell. I also found that a trip to Gomorrah and handing over all my weapons, then stepping outside, rids companions of their duplicate weapons. ED-E's default carried weight dropped back to 1, Arcade's to 10. None of the other casinos do this (I tested the Ultra-Luxe, and I'd progressed to a point where the Tops no longer asks me to remove my weapons, so I couldn't test it there).