People started referring to Glock handguns with extended magazines as 'Gluzi', being short for glock-uzi.

The Uzi is another gun with a commonly extended mag that pokes out the bottom of the grip, hence the comparison.

The slightly derogatory 'Gluzi' became 'Glizzy'

Now, another more derogatory nickname for a gun with a mag that sticks well beyond the handgrip was "Hotdog" because, well it looks like the sausage sticking out the end of a hotdog bun.

So people are calling these guns "hotdogs" and "glizzy", and so naturally, at a barbecue somewhere where the sausage was notaby longer than the bun, someone must have started referring to their extended sausage hotdog as a "Glizzy" as a joke, comparing the sausage to the extended mag of a Glock, and it stuck. The comedy lives in referring to an innocuous food item as a weird looking, often gang or crime-associated style of gun. Maybe because there's a high chance of encountering both kinds of Glizzy at certain barbecues, and bystanders are subject to the ol' switcharoo when one person asks for a Glizzy, and received a hotdog. Or maybe they asked for a hotdog, and recieved a gun, IDK I wasn't there.