So while I cannot give exact reasons for why different Bronze Age peoples such as the Egyptians or Greeks used the particular swords they did, I can give an explanation concerning the mechanics of the leaf-shaped blade and why it was the favored style of so many civilizations.

First of all, the main attraction of the leaf shape is that it gives a very good point for thrusting attacks, which were very effective in the fighting formations of the Greeks and the later Romans, who based much of their warfare on the Greeks. Since the point tapers out and then back in, it causes a very wide wound, which when delivered into the abdomen would cause a lot of bleeding and potentially tear the intestines, an almost certainly fatal wound at that time. Further more, once the thickest part of the blade has pierced the target, there is no further resistance being added due to the lack of additional blade contact. The Greek xiphos in particular was theorized to be used by soldiers in the more backwards ranks to finish off wounded soldiers that the phalanx moved over if the soldier had lost his spear.

As for my second point, by putting more of the mass further from the handle, there is more energy at the end of the weapon as well as serving to reduce the contact area at the beginning of the strike, much in the same way as an ax or a mace. This would make the weapon a bit more difficult to swing and harder to control, but would also increase the power of swings. While swings were uncommon for actual fighting among the Greeks and Romans, they were sometimes used, and to good effect.

Finally, a leaf-shaped blade would be easier to make out of bronze, since bronze weapons were mostly cast from molds rather than being drawn like iron. A leaf shape would be easier to make into a mold because imperfections in the shape would not matter as much nor be as obvious, though the latter is merely a conjecture since I have never seen a hand-crafted mold for a sword. Given the tools and technology available at the time, it would most likely have been easier for a smith to make the bronze blades with an approximate leaf shape rather than an approximate straight shape.

I apologize for not having a source for this, and I can attempt to find one if you would like. Most of the information I provided concerning the blade itself is based on the physics of the shape, which is much more within my knowledge base, so again I apologize if anything concerning the historicity of what I said was wrong.

Edit: if you have any further questions concerning the science behind weapons and why one type was preferred over another I would be more than happy to respond when I have the chance.

I couldn't easily find an answer on Google, what does it mean to call a sword "leaf shaped"?