When you fire a gun from the double action (hammer down) position you must compress the hammer spring with the pull of the trigger. When you fire from the single action position the hammer spring has already been compressed manually and all you have to do with the trigger is break the tension between the sear and hammer.

A double action firearm can be fired in either mode so I don't understand why you would avoid one simply because of the heavy pull from the hammer down position. You can always cock it manually. Being a double action firearm it provides you with a very quick means of recocking the gun should you experiance a misfire. Pull the trigger again and the firing pin strikes the primer again. Basically you can simply pull the trigger until it goes bang. In a single action gun you will have to either manually recock the hammer or manually rack the slide in order to get it to go bang. Much much slower for most people.

Now, a double action only firearm you can only fire it from the hammer down position and must compress the mainspring every single time you pull the trigger. Unless a person is practiced it this type of firearm it tires the trigger finger quickly and is usually much less accurate.