It's the other way around. That's why some manufacturers make their shorter putters heavier than the longer ones. In my opinion, putters are to heavy nowadays. I'm looking forward towards when the trend of heavy putters comes to an end, and a new 330g putter will be widely available again!
The shorter putter changes the swingweight and feels heavier.
Obviously the total weight of the putter is lighter when it is shortened however the swingweight changes when you shorten the putter. For me, I FEEL the head of the putter as heavier even tho the head of the putter still weights 330 grams. Semantics really but just lets agree it changes the feel.
My preference is a heavier headweight for very fast green. I have heard the oppisite from a few different putter guy mouth. I current put best with a 363g putter on fast greens (plus 10 on stimp). All preference of the archer and his arrows.