Who out there hates being tired?
(I see everyone raising their hand. Yeah, me too.)
Who out there is tired right now?
(No hands dropped? It's a big club, we should get t-shirts.)
My suggestion is this: use it. Own it. Take weariness by the horns and turn it into words. ...Dramatic and cliche advice aside, I'm telling you to write. I do my best (and most) writing late at night, when I'm too tired to be distracted by anything. And, also, when I'm too tired to care about every little mistake. Those can be edited out later, once the words are actually written.
Or sleep. Sleeping is good too.