Are magnetic compass acceleration errors due to the southern side of the compass being weighted?
Some compasses are counterweighted to decrease magnetic dip. Older and/or cheaper compasses for land navigation are this way. Many to most are not weighted, especially in aviation compasses. Weighted compasses would require different compasses for the North and South hemispheres. Instead, aviation wet compasses are built with the low friction mounting point above the CG and magnetic bar. This causes the CG to move to the South polarity end of the compass assembly when the magnetic bar dips downward to the North Pole and to the North polarity end when dipping towards the South Pole. I like this article that explains this phenomenon.

Several decades ago, my unit had the opportunity to train with the Australian 3rd Para Regiment in Australia. Many of us had been using personally owned GI lensatic compasses because the tritium markers worked better than the newer, issued lensatic compasses. We were warned that the older models may not be accurate down under due to them being Northern Hemisphere compasses instead of the universal ones. I did not understand the reasoning for this until many years later.