Of course you can, and plenty of kopis/falcata apparently had pretty narrow blade compared to most of "typical" ones.
Making it more narrow also in no way forces it to be lighter, either, as there are still two more dimensions to work with.
Cross-section, and general thickness distribution, will be as always most important.
Most antique falcata I've seen anyway had pretty elaborate fuller/groove work near the spine or even up to the middle of the blade - which certainly reduced the weight quite a lot