From the published BB9 numbers (the first ones I found using google), ratings routinely dropped, then increased, then dropped, then increased all season. There was no "consistent build" whatsoever. 8% drops were not uncommon at all.
Reagrding early season vs. late season..., the 1st, 3rd, and 7th episodes (all early in the year) were the highest rated of the entire season (taking away one or two freak numbers caused by terrific lead-ins from live sporting events like NCAA basketball). In addition, the first show had over a million more viewers than the final show.
You are right about season 8 though... it did seem to build audience very late in the season.
Although... from a wiki entry on season 8, it stated that "Tuesday shows are typically the highest rated among the three episodes every week, with Thursday in second and Sunday, a competitive night in television, in last among all three recap shows.". Which means a drop from Tuesday to Thursday is to be expected and probably had nothing to do with Chima.
I don't see any evidence Chima was a ratings winner and losing her somehow affected the show negatively. I think its more a combination of ALL the interesting personalities (aka "villains") being evicted (Chima included). It's like Star Wars with no Darth Vader. Incredibly boring. Jeff and Jordan are among the most bland personalities in the history of television.
Can you give a link for those BB9 numbers? Except for some laziness this season, I've read the ratings for every single show since BB1 (premier of about 10mil!), and a drop of 8% from Tues. to the eviction show (Wed. or Thurs.) is highly unusual in my memory. As I recall, the biggest you'd ever see, once audience was building, was maybe 5%. And the general trend of building throughout the season, at least after the first week or two has always been clear. As I recall, it would settle in around 5.5-6 million by week two or three, then creep up consistently to 6.7-7.2 million, except BB8 which climbed to 8 million, when you had the ongoing Evel controversy. Unfortunately, TVByTheNumbers.com doesn't maintain a complete archive, and before 2007 I was using other Nielsen listings that aren't available anymore. All I can find are a couple for BB10:
Thurs. 9/11/08: 7.818 million
Tues. 9/09/08: 6.98
Thurs. 8/28/08: 5.969
Tues. 8/26/08: 6.284
It's not that Chima herself is personally the ratings winner or loser, but that with her ouster there's no more strife and controversy and accusations of racism to promote the show. You don't need a lot of people for that, just the right people. BB11's build to 8 million by week 6 is striking, as is the Thursday drop to 7.33 million, but the rest of the season's numbers will tell whether the show's general audience has truly jumped 15% to 8 million from 7 million. I think Lydia was ripe for some bigger and better wacko acting out and could have held the show at 8 million, but now we'll never get to see that promoted.
America's involvement interestingly can go both ways. It ruined BB1 by indulging in the joy of ejecting the nut jobs and leaving us with a group of fuddy duddies. But then it made BB8 by forcing Eric to keep Evel when obviously (and by his own admission) Eric would have joined the house in ejecting him. America didn't suddenly love a villain there, but loved a villain with a softer (Danielle) side. Generally, though, America's involvement is fun for a second, then leaves us with crap.