Urchin summed it up quite nicely, but to add my little piece of 'snake feet'(
Asian metaphor meaning 'needless additional info' ):
If I remember correctly, the G series of the 109s are one of the most complicated series with vast line of modifications and customization. Of those, our 109G-6 is the most 'standard' factory type introduced in early 1943. It is the heaviest of all 109s, and as Urchin said, increase of weight was due to heavier armament of MG131 7.92mm guns. I'm not sure if there were any additional changes such as increased armour, but one thing for certain, the MG131s had some problems when it was fitted into the cowl. The protruding bulges or 'warts' had negative effect on aerodynamics.
One of the positive changes were the increase in visibility via introduction of the Erla Haube(canopies with less frames) and Galland Hood(transparent armoured glass behind the pilot's head), but this factor is not very prominent in AH since the rear view is very lenient anyway.
The result, as Urchin said, with limited power + added weight + aerodynamic problems is our G-6. Slower than a G-2, top speed is almost the same as the 109F-4 around 387~390mph (introduced in 1941). The G-6 maneuvers the worst of all 109s, but like other 109s it is very forgiving and unbelievably stable even at low speeds with a gentle stall.
One very positive factor for the G-6 is the G6/U8 type armament with the MK108 30mm nose gun. One hit knocks an enemy plane dead with almost 99% probability. Of all my fights with MK108s, I have only seen two cases where the enemy survived a hit. (One was a 650 yard lucky hit on a La-7 which knocked out it's flap, and the other was on a P-38 at 260 yards where it lost it's left engine only)
Now, the G-2 maybe agile and more capable a pure 'dogfighter', but since it won't be able to slug it out with planes like Spitfires anyway no matter how agile it is, anyone flying 109G series would probably be subjected to strict Energy tactic principles. And if that is the case, provided one's gunnery is above average, flying the G-6 which can destroy the target at a single pass might even be a better choice.
Making a real critical hit on a single pass with the G-2 is harder and it prolongs the fight where often even mere 30 seconds can determine the outcome. I've had a lot of cases where I up a G-2, fight the enemy to the bone, land a few hits but had to extend away because the fight was taking too long and enemy reinforcements arrived. With the MK108, a rotte of two G-6s can be even more deadly than two G-2s.
I've had some lessons with Frenchy some months back, when I couldn't seem to find anyway to fight P-51Bs with alt advantage in a 109G-6 at the Combat Theatre. Frenchy kindly took up a 109G-6, and I upped a P-51B and he showed me a few pointers in fighting against Allied(especially USAAF) planes.
Fortunately I have those films, and I can e-mail it to you if you are interested, bozon. I asked Frenchy a lot of questions that time and all of those questions are recorded in the film too