i. ?I am sat
ii. I am sitting
iii. I am seated
(? denotes questionable grammaticality)
In [1ii], the gerund-participle sitting is just a simple verb -- indicating that the subject is sitting.
In [1iii] we have the past participle used in what The Cambridge Grammar of the English Language calls the ascriptive use of be (a kind of copular clause).
[1i] sounds wrong. Is it wrong? No. It's just not standard usage.
In the ascriptive use, PC [predicative complement] denotes a property and characteristically has the form of AdjP or … NP.
That is, an ascriptive copular clause takes the form NP + be + AdjP (or + NP, but we definitely don’t have an NP here). A verb can be inflected to be used as an adjective by using the gerund-participle form or the past participle form. Sat is the past participle of sit and thus, unless I’m missing something, [1i] must be grammatical.
This, of course, does not apply when the preterite and past participle are not syncretised.
Consider the following:
 *I am want [preterite]
ii. I am wanting [gerund-participle]
iii. I am wanted [past participle]
[2i] is ungrammatical, while [2ii] and [2iii] are fine.
In summary, I am sat is an example of the ascriptive use of be.