On my clousers I tie in med size chain bead eyes rather than say dumb bell eyes that weigh more. So they are rather light but still sink, they actually give the fly a nice moderate fall rather than a diving motion and it allows me to retrieve them a little slower and it drives the fish nuts. Anyway they are no proublem what so ever to throw.
I tie them with various barbells & bead chain too. I also like that slower fall rate that bead chain gives for some of the shallower waters I fish. I also like to move the eyes down the hook shank a bit. Makes them look a little odd sometimes, but changes the way they fall. Allows them to glide, particularly with lighter weight eyes rather than dive as you've described.
Here's some I've tied. Basic chartreuse & white in size 1. The hooks are Daiichi straight shank worm hooks, the eyes are brass, and colored black with a Sharpie. I then coat them to prolong the color from getting rubbed off. The fish don't seem to care either way. These have "Rainbow" colored Krystal Flash & gold holographic Flashabou in them.