My first consideration when making any slingshot is whether the materials used and the design chosen will be strong enough to handle the intended flat band sets or tubes: catastrophic structural failure is simply too dangerous given the potential of high velocity debris nailing your face in the midst of shooting action. :hmm:
Thus, keeping weight down really boils down to a sound combination of suitable materials and appropriate thickness of these materials where this is essential. The problem with any type of wood is its inconsistent internal grain structure, which may or may not be visible externally before you start making a slingshot. Moreover, that nice looking natural fork may have been subjected to some degree of internal wood rot, which will have created weaknesses where you do not want them.
Generally speaking, it is always a good idea to place the natural fork inside a vise, and to apply some serious tension with the hands (wear working gloves) or attaching some rope to the forks and pulling hard to see how resistant it is. Better safe than sorry, right?
By definition, a very compact sized natural which has a relatively thin branch thickness should be fine, but that thickness needs to increase more or less proportionally the longer and wider that natural fork becomes: a natural frame with thin branches and high forks is more likely to break unexpectedly due to leverage effects. Think weight (thickness) vs. safety.
The same principle also applies to metals, but at least here you can assume that its molecular structure is generally very consistent, along with ample information about its structural properties and behavior when stress factors are applied. Chances are that metal will be on the whole far more forgiving than wood. Plastic is another ball game altogether, particularly as it develops weaknesses when subjected to UV and temperature changes: it does not age well either, unlike wood. Caution with those 3-D layer printed plastic slingshots, the big new fashion to come.
Ultimately, if super lightweight is your prime objective, I would suggest taking a closer look at corrugated cardboard in combination with fiber reinforced adhesive tape: you can make a slingshot with this stuff anywhere you are, particularly if you forgot your favorite slingshot at home. You will be surprised at how strong the frame shown in the attached photo is.
Of course, do not get it wet...