Heavy Liquid Casting Resin

Kind of depends on why you are doing this.
If you are trying to balance an aircraft model on its nose wheel, forget it. The resin just isn't dense enough to get enough weight in the limited space available. You're better off pouring in small lead shot (sporting goods or gun store) and sealing it off with some resin or superglue.
I'm not sure what to do if you are just looking to make them feel more substantial (stiffer?). I'd be leary of any resin that can flow easily through small holes. Seems like it could also run OUT of small holes. Stay away from polyester (fiberglass) resin. It can generate a lot of heat when it cures in thick (1/2"?) sections. (Doesn't it also attack styrene?) I've heard horror stories about guys trying to pump polyurethane foam (that spray can insulation stuff) into finished models. It can generate enough pressure to split most model glue seams. A common technique for stiffening up large vinyl kits, is to use fill them with plaster or Durham's Water Putty (hardware store). Unfortunately, these aren't very runny and may not be easy to work into an assembled model.
Good luck,
Greg Reynolds, IPMS

Point to keep in mind, some resins give off heat when they are curing. Be wary of any resin if it's instructions say it is "exothermic" while curing.
Bill Shuey

That would be my suggestion too. Ordinary plaster of paris is essentially the same thing and with it you can make it very runny if you like but I'd leave a drain hole to allow bleeding off any excess water. Using a cake decorator's tool as an injector might ease the filling process.

I'm working on a movie, and what I'm doing is turning hollow plastic squirt guns into heavyweight "stunt doubles" for the more expensive guns. These need to be heavy so they can be dropped, tossed about etc. with the same physics as the real guns.
I've considered lead shot but worry that I won't be able to ensure even distribution inside the form. I tried wall putty, but it wasn't heavy enough (or I wasn't able to fill the entire area inside the form). I figure low viscosity resin will fill all the nooks and cracks, then harden evenly. Obviously, any filler that expands, heats up, or dissolves plastic is out.

"Obviously, any filler that expands, heats up, or dissolves plastic is out."
Resin tends to generate considerable heat during the brief but intense curing process. Might not be enough to melt down your guns, but I'll bet it is enough to distort them here and there.
Norm

Ahh....
If lead shot is too heavy, try sand.
Get a nice clean day coarse sand at the nursery. If it doesn't give you enough "heft", try mixing lead shot with sand (before you put it in).
Greg

I've been using bird shot, its smaller than buckshot and will fit into more small spaces. I usually mix it with some Elmer's Carpentry Glue (the yellow stuff, not white glue) into a reasonably stiff mixture, and then pour it into the area that I want to fill It brings all but the most stubborn tail-heavy models to heel and makes them sit properly.
-- John The history of things that didn't happen has never been written. . - - - Henry Kissinger

"Obviously, any filler that expands, heats up, or dissolves plastic is out."
20 minute casting plaster! It stays cool, doesn't expand, doesn't harm plastic, and it's cheap...

I find that plaster does gets warm. It's more noticeable with large castings. But it doesn't get as warm as casting resin, and not enough to harm a plastic model. Plaster also tends to cool down quickly after a certain point, probably due to evaporation of the water.

The filler needs to be low viscosity enough to flow into the form through relatively small openings: 1/2" or so at the small end of the spectrum. My feeling is that if plaster were thinned enough to do so, it wouldn't dry heavy enough.
I don't have a lot of experience with plaster (besides spackling my walls) so I'll defer to the expertise of others.

Plaster is simple and you can buy a 50 lb. bag for about the cost of a quart of casting resin. I use it at work (modelmaker) all the time for filling vinyl tubes (squeeze type) and empty shampoo bottles to make them rigid and heavy for painting. They are smallish (as is a squirt gun) so heat generated isn't a problem. I usually only mix about 20 oz. at a time and use cold water to keep the heat down further. If your mix is smooth (I sift the plaster into water to avoid lumps) it can squirted through a syringe or poured through a funnel. If you do choose casting resin, you may want to try refigerating it before mixing. This will slow down the gel time and help with exotherm, but will thicken the mix... Good luck Zactoman

I've heard of folks doing large vc models filling them with the same sort of expanding foam that UPS uses to form-pack packages with.
You have to be careful and leave an exit for the foam to expand out of, and make sure to not over fill and blow out the model.
Here's Ian's example from his 1/32 Connie build on his 1/32nd Sig site:

If ya look long and hard, ya can find Dust. It is the finest lead shot made for shotguns. Havnt seen it in a while, but it was fun in the old days to load a bunch of shotgun shells up with it and shoot at each other at say around 70 yards away :)
Anyway, if you can find it, it is the best for adding weight to something. (a friend has an fired APFDS tank round, now thats real heavy :)

Wow, now that is an impressive project !!!!!!!!!

What about the new foaming polyurethane glues (ie Gorilla Glue), mixed with bird shot?
I've found Gorilla Glue to be about as thin as honey, but if its warm, it can get thin. One advantage to using this type of glue is that it foams when it cures, so that would help lock the shot into place.
Ken

They aren't exactly new, Gorilla glue has been around since the 80's at least. They also tend to blow thing apart when used to glue in filler or shot, if there isn't sufficient venting they will take apart a squirt gun.