Point weight affects balance, or FOC as it's known and calcualted now. Basically, yes. A heavier point will make a more accurate arrow if the overall weight of the arrow isn't too much and the dynamic spine hasn't become too weak. Some bowhunters prefer a VERY high FOC, escpecially with carbon arrows. With wood and other arrow materials you should find it isn't as necessary. Cane, being light and rigid as well, might also benefit from a high FOC.
The "sweet spot" is 10%-15%. To find your FOC find the balance mark. Measure from that point to the middle of the arrow (from the throat of the nock to the back of the point). This should be a few inches, let's say 3". You then divide that by the arrow length, let's say 30", and get your FOC- 10%. That's acceptable.
An example of what an effect FOC has: I had a set of arrows. With 125 gr blunts they flew wonderfully! As soon as I point similiar weight broadheads on them... all over the place. COuldn't call my shots at 15 yards! I switched to 175 gr points and, even though they are slower and won't shoot as far, they are more accurate now.