Does the sentence mean the same even after I put an as before the word tired as follows?
Tired as I was, I worked overtime.
As tired as I was, I worked overtime.
(an adverb clause meaning Although)
Could you help me clarify it?
The traditional form is Tired as I was, ...
But you do now encounter As tired as I was, ...
I believe this arises from a blend of the unfamiliar syntax with the more familiar as tired as.
Looking at the Corpus of Historical American English, I find 575 instances of "[adj] as [pron] was", and up to 1900 there were at least 35 per decade, but only 7 in the 1990s and 12 in the 200s.
On the other hand "as [adj] as [pron] was" has 85 instances, but more than a third of them since 1990. It never had more than ten instances in any decade until then; but had 16 in the 1990s and 19 in the 2000s.
So in this particular corpus, the form with AS was rare until around 20 years ago, but overtook the form without AS in the 2000s.