I have .44 Special and .44 Magnum revolvers. I think the .44 Special is a great cartridge and so is the .44 Magnum. The last time I checked the 24-3 or 624 in a 4" barrel (41 1/2 oz.) is 1 1/2 ounces less than the 29 or 629 with a 4" barrel (43 oz.). In my mind, the difference in weight is negligible and doesn't really make the .44 Special that much easier to carry.
If you handload, you can shoot reduced loads in the .44 magnum or shoot .44 Special loads. You can also shoot hot handloads in the .44 Special that approach the .44 Magnum.
Could it be that the .44 Special with the tapered barrel justs looks cool?