I am not quite sure what you are getting at, but average round weight is 23.7 g (366 gr). If you want to know bullet weight of the British Army ammunition issued at Bisley, it was 144 grains.
The 168 gr BTHP you mention is probably the M852 round. The late Roy Meketa wrote about it:
“The long awaited M852 proved to be somewhat of a disappointment. The 168 grain bullet, with its short 13-degree boat-tail, was a modified International Hollow Point that gave very good accuracy out to 600 yards but was found lacking at longer distances where velocity went trans-sonic and suffered a significant reduction of accuracy”
William C. Davis Jr. reported similar observations in the American Rifleman. A heavier bullet is not automatically superior at longer ranges.
Edit: The loss of accuracy is due to a loss of stability, due to aerodynamic effects. Every bullet behaves a little different, suffers different drag and consequently the consistency from shot to shot suffers. The 144 grain FMJ remain more consistent from shot to shot and show better accuracy.