Go ahead, cut off that handle that you never use anyways.
The Jetboil cooking system is a great way to boil water on the trail. It might be a little heavier than some other ultralight cooking options, but the fuel efficiency makes up for that in a hurry. Furthermore, with just a few slight modifications, one can shed 4 - 5 oz. from their Jetboil weight -- making this cooking option truly the best one out there.
The weight of a Jetboil Sol out of the box is 14 oz. for the aluminum version. This includes the 0.8 liter cup, cup cozy, stand, burner, lid, and bottom protective/measuring cup. Some models also come with a skillet stand for the burner. Not all of these pieces are necessary, and leaving a few of them behind can provide an easy way to free up weight.
The first thing to toss into the camping gear junk drawer is the stand. The fuel canister alone is adequate enough to stand up the stove on flat ground or a flat rock. If worst comes to worst, one could even hold the stove in their hand, but certainly this wouldn't be necessary.
The next thing to leave behind is the bottom protective/measuring cup. Sometimes it's nice to have an extra dish in the backcountry, but it's also easy to do without, and definitely unnecessary.
Leave your Jetboil stand, bottom cup, and skillet stand behind to save some weight.
If your Jetboil came with a skillet stand for the burner, leave this behind as well. Even if you're using a skillet, it's likely you won't need the skillet stand. Sure, it's a nice luxury to be able to set the skillet down while cooking, but if you're using an ultralight titanium skillet, then you'll probably have to hold the skillet over the heat in short or medium timed spurts as not to overheat it anyways. And you can always set it down on the ground or a rock for a moment while tending to something else. Most backpacking meals made in a skillet are cooked rather quickly as is, so the skillet stand is unnecessary.
If you lose those 3 items you'll have shed 3.5 oz. -- that's 25% of your Jetboil's original 14 oz weight!
Getting even craftier, you can take off about another half ounce by cutting off the handle on the cozy that you don't use anyways. Now your stock Jetboil Sol weighs just under 10 oz.
Stopping here is fine. You've already produced a 28.5% decrease in weight on your camp stove, which is awesome. If you wish to go even further, it is possible to take off another 2 - 3 oz., but it may end up costing you in fuel efficiency and durability of the stove.
The Jetboil cup, burner, and lid are all that are needed to create the perfect storm of ultralight efficiency.
You can save just under an ounce by leaving the lid behind, but boiling water without the lid will take a little longer which results in more fuel consumption.
Another savings of just under an ounce can be accomplished by removing - or breaking off - the plastic orange ignition system and wind screen which is attached to the burner. You'll then have to light your Jetboil Sol with a lighter or match, and losing the wind shield could be regrettable in certain situations.
Lastly, the Jetboil Sol also comes in a titanium model which is 1 oz. lighter than the aluminum. The caveat is that the titanium is reported to be much less durable, particularly the heat distribution fins on the bottom of the cup which are exposed if you leave the bottom protective/measuring cup off. For this reason, the aluminum version is worth the extra ounce of weight for its superior durability on the trail.