There are good answers here already, and yes, proper composites would work best, but may need better tools to be build, so here's my spin on it. Thus let's look into Types, Performance and Curing of resins.
Types of resin
There are natural resins that get hard and there are natural resins that get rubbery. Commonly they loose water and terpentines in the process, but they may also polymerize. Hardened resine doesn't rot quite as easily, and may become amber under certain circumstances.
Performance and Usage
If you have mainly soft wood, it may outperform that. HOWEVER: Keep in mind that in the comparison "laminated wood" (plywood) vs fiber-composite vs pure resin, the pure stuff will lose as compounds are usually superior.
Plywood is far more difficult than fiber composite, as you must get it very even. If your resin doesn't really harden, but only gets semi-hard and sticky, it may be better than fiber composite.
For hard resin, fiber composite is probably the best to build, as it is easier to form and probably stronger as well.
Also: While if used like glue, plywood is an option, the question arises, why not to use the wood itself. A possible reason might be your plants: They might have good wood, but bad growth patterns. Making a composite may enable you to form it appropriately.
If (partially) transparent, the resin might be used for decorative reasons. Especially on spears and bows, if you use fibers for the composite, you might form it to build some holes in a decorative pattern, which may be filled with the resin and thus still provide (some) compressive strength.
It might also be used as shards-section in a weapon. If you have a spear, and the cured resin is a bit brittle, one might use it to attach break-away tips or to outright build a shard-tip to maximize damage to prey or opponents.
Sharpness of your weapons might also be a reason:
If we argue that you have only chalky stones, you might have a hard time getting a proper point to your spear. Especially when you have no access to hard woods. A bone will crack, yes, but it will not give a sharp edge. As the stones are soft, they won't give proper blades either. Also they are to soft to grind bones or wood to a point on them. You may break of strong-ish branches, but again the end will feather out and be difficult to be ripped in a way that produces a point. The result would be a spear with a rather meek tip. Hard resin or rosin to the rescue: you create a spear the old way, then dip the tip into hot rosin and let it harden. If you left it hanging tip-down for hardening, you already got a better tip than before. However, one may improve on it, if the resin is also at least a bit brittle. The tear-drop tip may be broken of and (at least for many types of rosin on earth) will form a semi-sharp to sharp edge. (Rosin is usually quite amorph and thus may crack building sharp edges. Think of rosin as a bit like a mix between the strength of most plastics and the shard production of glas.)
Curing your resin
At some point you'll want to cure your resin.
There are a few options, each with their pros and cons.
Cem Kalyoncu argued you might mix two or more saps and resins for them to react and harden. On its own, this would probably result in inferior plastics, caused by impurities naturally occurring in the saps / resins. HOWEVER you might wash it during reaction, getting rid of impurities and thus better quality.
Alternatively you might cure with white ash or charcoal, but again washing might bring improvements, as might folding.
Two possible settings:
- Mixing results in granulate matter, which after washing may be used (probably by melting it)
- Mixing results in something that feels like a mix of bubblegum and honey. While washing you fold it and stretch it, rinse and repeat. The result may be formed like clay and will slowly harden.
It might well be, that a certain plant has sap that will harden when exposed to air to clot a wound. The reaction would stop close below the surface as new air has a hard time reaching in. Thus your craftsmen might pull it apart and fold it, or if it's thin and runny, whisk it to bring it in contact with a lot of air. It would probably build a gooey foam that will start getting warm. You could then form it. Again, working it in water would keep it cold (probably slowing down the reaction), clean out impurities and might help removing the bubbles.
Similarly, a plant might have sap that hardens when exposed to sunlight. Thus your workers might harvest it at night time. If transparent, this might be casted and left in the sun for a few hours or days to cure. For a compound, one might wet fibrous material with it and hang it in the sun to cure; subsequent layers could be added by painting them on.
NOTE: Neither the light nor the air version will work terribly well with cross-laminated wood. Air would probably work better, as it might get saturated before hardening, but both would need fast working.
So far, the results will most likely NOT compost. Let's address that.
You may boil resins to make rosin / colophonium. Rosin is hard and plastic like. Basically it is the remainder of resin, after water and terpentines boiled away.
Furthermore there are rubbery resins (usually not from the plant sap, but from the fruit sap) that work to make it flexible (latex, kauchuk, plum-resin).
By mixing these resins and varying the boiling times the rosin may be customized.
The resulting rosin will compost, but not super-easily. Of course adding fibers would make it far stronger, but (if not overdone) it could be formed to build transparent sections.