This コソコソ (because katakana likes to be like that). The line probably makes a lot more sense for you when the word means “sneakily; secretly; stealthily”.
Let’s set aside the conjugation for just a moment, and look at the sentence without it. This will give us a baseline for understanding.
Marking the Indirect Quote
と here is marking an indirect quote, and 思う conveys that it’s what Big Brother had thought.
The sentence 「コソコソしてる」 is based on the verb する. It’s connected to いる (which for する, becomes している, and the い is often dropped when speaking).
The verb する means “to do”, and してる makes it a continuous action, “to be doing”.
Because する is a generic verb (like “to do” in English), there’s no indication of what is being done. However, the adverb コソコソ tells us how the action is being done. Something is being done “secretly”.
With that in mind, we can translate 「コソコソしてる」 as “To do secretly.”
The verb 思う, “to think”, is in its completed/past tense form: 思った, “thought”.
By adding と思った to the sentence, we have “I thought [indirect quote]”, so 「コソコソしてると思った」 becomes “I thought you were doing something secretly.”
Making it a Conditional
Next, we add ら to the end of the verb: 思ったら. This is one form of conditional used in Japanese.
What’s conditional? It’s where you have a condition. An example of a conditional in English is: “If I wash my car, it’ll rain.”
But we’re working with a completed/past tense action here, so a better English example is: “When I washed my car, it rained.”
My understanding is that when ら goes onto the completed/past tense of a verb, it has a sense of “When I did this in the past, I didn’t expect this other thing to happen.”
Let’s put this ら back on Big Brother’s sentence:
「コソコソしてると思ったら (I didn’t expect it was something like this.)」
“When I thought you were doing something secretly (I didn’t expect it was something like this).”
The part in parentheses isn’t being spoken. It’s simply implied. He’s leaving the sentence unspoken (as seems to be done often in Japanese). He doesn’t need to say the second half, because Kanami knows what he’s talking about.
If I was too rambling and unclear, let me know and I can try to simplify it a bit.