[MarkSheppard]

because the MMG is mounted on a bipod and is prone to shaking when firing, reducing accuracy.

Meanwhile the HMG version is mounted on a 15 or 50 lb tripod. The 50 lb tripod had a lot of cool features:

The larger tripod, the MG 34 Lafette, included a number of features, such as a telescopic sight and special sighting equipment for indirect fire. The legs could be extended to allow it to be used in the anti-aircraft role, and when lowered, it could be placed to allow the gun to be fired "remotely" while it swept an arc in front of the mounting with fire, or aimed through a periscope attached to the tripod. Mounted to the Lafette the effective range of the MG 34 could be extended out to 3,500 meters when fired indirectly.[8]

Another unique feature of German World War II machine guns (which continued to be used by the German Bundeswehr after the war) was the Tiefenfeuerautomat. If selected, this feature walked the fire in wave like motions up and down the range in a predefined area. E.g., being unsure whether the real distance was 2000 meters or 2300 meters, the gunner could make the mount do an automatic sweep between the elevations for 1900 to 2400 meters and back. This sweeping of a given range (Tiefenfeuer) continued as long as the gun fired.

EDIT: Tiefenfeuer may sound liek it's over complicating the tripod/gun design; but there's a very good reason for it. It makes the movement of the machine gun mechanical, instead of depending on the operator.

An inexperienced machine gun operator who doesn't have the training or experience necessary for the job will tend to focus his machine gun fire on groups of infantry.

It's counter-intuitive, but to be effective, a heavy machine gun can't afford to concentrate on individual groups of soldiers. What you have to do is to create a 'beaten zone' by raking fire back and forth that ensues that nobody moving there can move without risking a 50% or more chance of injury; so this means that you have to counter intuitively move the machine gun away from groups of soldiers to complete a sweep of the beaten zone, before swinging back across them.