I am trying to decide if negotiating to delay the start of a TT position in order to complete the 2nd year (out of 2) of my current postdoc is a good idea. I am mostly interested to hear your thoughts on the benefits/disadvantages to do this in regards to obtaining tenure. I'd like to specify that this postdoc involves teaching (two courses), and (it is very likely that) I would have to teach the same amount of classes for the TT position in my first year. I have a good number of publications set to appear next year so I assume that would be good for tenure.
Sorry that I missed this earlier, and hope an answer is still relevant.
The purpose of a postdoc, actually, is to enable you to get a permanent (eventually) tenured position. They help you build a research portfolio that gets you recognized as a potentially valuable member of a permanent faculty. But, otherwise, it has limited value for a career as an academic. There was a time when such positions weren't common and it was easier to move directly from degree completion to a regular job.
As such, delaying seems to be a mistake, especially if it puts your eventual position in doubt in any way. Things change in universities. Offers can potentially be withdrawn if economic factors affect the university.
In most fields, continuing research started as a postdoc is possible so that may not be a problem (some lab sciences might be an exception, as would some confidential work).
My advice would be to take the TT position without delay, provided that you can leave the postdoc on good terms.