I shoot a 223 but just for personal pleasure, not competition. Nevertheless I strive for the tightest groups and can offer the following.
I have weigh sorted brass and never noticed a difference on the target, but I have trouble shooting consistently below 1/4 moa anyway. Maybe it will matter to your particular skill level. I prefer to buy my brass, as opposed to picking up range brass and keep it segregated from other brands, lots, purchases. I prep it carefully, but no longer weight, or H20 check it.
Measuring bullet OAL is a fools errand as they vary wildly . Measuring base to ogive is standard, but IMOP not much better, although some will argue that. I will measure mid boat tail to ogive using two Hornaday OAL inserts. But again, in a 223, the difference in case intrusion is not going to show any measurable pressure changes until you're shooting competitively at 1000 yds where vertical dispersion will be deadly to your game.
FMJBT are not known for accuracy. An open tip match or plastic tip match, especially the 53 gr. V-Max or 55 V-Max will shoot much better, IMOP. I shoot the 69 gr. Lapua with good success. If your barrel is an 8 twist, you can shoot the 80 SMK which is another good bullet.
For excellent consistency, neck tension is key. The better you are at sizing the neck precisely every time and with not too much tension, will quickly become apparent on your targets.
Tell us more about what you're shooting, barrel, twist, throat, brand. Also your loading equipment and measuring tools.
Almost forgot: Welcome to the forum!