Use it when something confirms your suspicions or expectations, but don't overuse to avoid seeming like you always expect the worst. I heard he got the promotion because he's related to the boss, and I thought as much!
Pro Tip 2/3
Not Surprised
Express lack of surprise in a situation where others might reveal the information as though it's a big reveal or new discovery. There was a storm last night and your flight was delayed? I thought as much.
Pro Tip 3/3
Subtle Agreement
It's a soft way to say 'I already knew' without saying it directly, which can seem confrontational or arrogant. You've been feeling under the weather after all that rain, haven't you? I thought as much.