Lighter bullets are usually paired with faster powders. Hodgdon says H4895, Varget, or H335 for the 125 gr bullet in 303 Brit. H414 is a slower powder better suited to the heavier bullets. But if you were to get H335 it can be used for both the 175-180 bullets and the 125 gr bullets.
This pairing is usually because you can not get enough slow powder in the case with a light bullet to get max velocity performance.
I reload for over 30 different cartridges (from 22 Hornet to 45-70) on a progressive press that really like spherical powders that meter better through the Dillion powder measure. I use W231 (same exact powder as HP38), IMR4227, H335, H380, H414, and sometimes H870. Those powders cover almost all 30+ cartridges.
Gun barrels are given a twist rate for the bullet weight expected to be shot in them. The heavier the bullet the faster the twist rate has to be to gyroscopically stabilize the bullets so they don't key hole in the target from tumbling in their ballistic path. When you shoot lighter bullets in the fast twist rate they are over stabilized which is not a problem if they can stand the excessive RPM's without flying apart (been there, done that!!). For example a bullet traveling at 3000 Ft/sec in a 1 in 10 inch twist (150 grain 30/06 load) spins the bullet at 216,000 RPM. Be prepared for the 125 gr bullet to maybe fly apart and have terrible accuracy.
Finally, don't ever experiment with loads outside of the manual published loads or the Powder/Bullet company internet loads. That means no loads from your buddies or some guy on the internet. If it is not published by a reloading company then don't use it! Break out of the norm and you may get a visit to the local hospital or loose the gun.
LDBennett