BIG 10 -3 teams
Pac12 -3 teams
BIG 12 3Teams
SEC - 3 teams
BIG East - 2 teams
ACC - 1
WCC - 1
Interesting question. It is hard to compare conferences in the regular season, since interconference play is essentially done by Christmas. So if a team is improving through the season, that doesn't get reflected in interconference comparisons.
That's an issue in comparing conferences just on the number of teams that make the NCAA tournament, as that count is based on regular season performance, and interconference competition stops in December.
Counting teams in the Sweet 16 at least allows you to have 2 rounds of Tournament play to compare conferences. But that comparison is also heavily dependent on seedings in the bracket. Some conferences, due to better seedings, may have easier paths to get more schools into the Sweet 16.
The other problem with counting teams in the Sweet 16, is it is a very small sample. With only 16 schools and 6 major conference (P5 + BE), you'd expect each major conference to have between 2.33 and 2.67 schools in the Sweet 16 (depending on whether you expect 0, 1, or 2 mid-major schools). So is there a real difference between the BE getting 2 and B1G getting 3, or is that just a rounding error or random chance.
I think of all the rounds in the NCAA tournament, the Sweet 16 is the best proxy for conference strength, because it provides the best balance of interconference play post-December and large sample size. But being the best proxy doesn't necessarily make it a good proxy.