I have an update that might be helpful to others. (I'm running iOS 9.3.) Weibo wouldn't show up in my app unless I was logged into my Weibo account in Settings / Weibo screen. (Just like you need to be for Facebook or Twitter.)
You do not need a Chinese keyboard installed.
Interestingly, I also found that simply installing a Chinese keyboard will make "Tencent Weibo" show up as an activity in stock apps like Photos, but that wasn't enough for my app. In any case, if you choose Tencent Weibo and are not signed in (on the Settings / Tencent Weibo page) then the user will get an alert explaining that they need to be logged in.
Of course, all of the above assumes that UIActivityTypePostToWeibo and UIActivityTypePostToTencentWeibo are NOT listed in the excludedActivites array.