"to suspect" vs "to be suspicious of"
In many contexts, both forms mean exactly the same. But I think #1 would occur more often.
1: I'm sorry for suspecting you.
Strongly implies you suspected someone was guilty of some specific misdeed.2: I'm sorry for being suspicious of you.
May be used in contexts where you had more general misgivings about the moral character or motives of a person, though it can also (perhaps less commonly) be used in the same contexts as #1.
Another specific example of a difference; suppose you download and install updated video driver software on your computer, after which your computer keeps going wrong...
The driver is suspect (I think it contains bugs that are accidentally causing my problems).
The driver is suspicious (I think it contains malware that is deliberately harming my system).
Latin suspectus, perfect passive participle of suspiciō ("mistrust, suspect"), from sus-, combining form of sub ("under"), + speciō ("watch, look at").
Given the identical Latin root, there's little reason for there to be a difference. In practice, using the term suspect implies they may have been responsible for something, whereas suspicious behaviour is less focussed. The term 'suspect' has certain legal implications, so the first might be seen as slightly stronger.
But that's a minor quibble - they're basically the same.