DAVE:
I used to be a dedicated bullet weigher.    If you think about what causes the variation in weights, you will realize that the bullets that are "lighter" are missing some metal somewhere.   This turns out to be voids near the center-line of the bullet.

To see what the effect this would have on the accuracy, I collected a batch (~ 50) of the "light" bullets, and together with some "full weight" bullets, and fired them (scope/bench) at a target with a grid of lines.   Each bullet was fired essentially at its "own" target, each bullet having its weight deficiency known.    The distance the bullet struck from its own "X" on the target was plotted on a graph,  weight deficiency VS distance from X.   

The result was not the expected "error" increasing with decreasing weight, as most bullets, even the defective "light" ones, struck at the aiming point, but there were a few slight fliers, in increasing numbers as the weight deficiency increased.  Note that "most" of the "light" bullets struck accurately.   And most of the bullets in this test were ones that would have been discarded as being "light".

Thorough statistical analysis showed that weighing ALL the bullets and discarding the ones that were "light" by a certain amount, would POSSIBLY eliminate as many as  1% of bullets that MIGHT be measurable  fliers.   This was an arduous experiment to do, obviously, but convinced me that weighing bullets is really a waste of time.

If it makes you feel good, go ahead and do it, but don't fool yourself that you are improving your results by a measurable amount.

CHRIS

I am not only a bullet weigher, but I am a dipper banger and a bag squeezer.  For each years matches, I cast somewhere around 800-1000 bullets from my ~209 gr (20-1) 3 groove spitzer. I sort them into .1 gr lots.  Assuming I have large quantities of bullets in the 209.0 to 209.5 range sorted, I will have enough 208.8-9 for serious practice and some less than 208.8 that I will shoot 3 or 4 to get the barrel up to accuracy condition.  I only lube them when matches start after casting from late fall to March or so.

the farther the shooting distance the more important weight becomes  at 100 or 200 yards not to important  at 600 quite important  art

I used to weigh bullets, but I don't anymore. I do still inspect all my bullets and toss any questionable bullets back in the pot. I also tested known bullets that were one half to one full grain light on heavier 410 gr. .40 caliber bullets and didn't see any measurable differences in accuracy from 100 yds. to 1000 yds. I do believe if there were dramatic differences it can affect accuracy, but those large differences will usually show on inspection as wrinkles, or rounded edges on lube grooves or bases.
I know shooters who always shoot in the top 5 or 10 guys at matches and tell me they also quit weighing bullets. So if they don't find it worthwhile a duffer like me surely wont.

My process has always been to leave my molds on top of my furnace while heating the pot up. Then once up to temperature I cast a bullet and set the mold aside for a few minutes to further heat the mold. I then cast 5 bullets and inspect each visually, and often drop some back into the pot if they look less than perfect. 
by the 5th bullet they almost always look perfect and then it's full speed ahead casting bullets. I do one more inspection of all the bullets once I'm done, and toss culls back in the pot if I find anything suspicious.

What’s the statistical significance of picking 0.3 grain, or 0.2 grains, or any other number?  I’ll tell you.  There is none if you randomly picked a number that makes you feel good. 

The correct way to determine outliers is to weigh all of the bullets, then calculate the mean and standard deviation, then throw out any that are more than 3 standard deviations from the mean.  Anything else you throw out is part of the normal population and you’ll be chasing your tail to get any accuracy gains.  Using proper 6 sigma limits to your data, you should throw out less than 1% of the bullets cast.  If the weight range seems too large, work on your casting technique rather than your use of the scale.   

Weighing the bullets in the order you cast them should give some insight into where your casting cadence and technique went south.

The bottom line is that with good casting technique the outliers usually have visible defects and are faster to cull with your eyes than your scale.   

Just my opinion on the misuse of statistical process control in bullet casting.

Since I keep track of the cast order, I will note ant time there is a forced break in my cadence and note the following bullet weights.  There is usually at least one lighter bullet following the break.  I also find that the sprue plate tension is important.  I prefer the plate to be a loose as possible without swinging freely.  Spring washers help achieve this desired tension.  I have a couple of moulds that tend to have to plate seize up as the mould gets hotter.  My solution is to touch a  slightly used birthday candle to the plate screw WITH a bullet still in the cavity. If I do it right I get back to my rhythm in a bullet or 2. 

Jack