What to do if you can't sleep but you're very tired and weary??

Not all feelings: of "tired and weary" are due to sleep deprivation, though that can certainly be a factor. Depression and anxiety are causes of all three of these. Do things to sleep better: strict sleep schedule, watch pre-sleep food and drink, wind down with soothing activities before bed. If you sleep better, see if you feel less tired. If not, you need to see your doctor for eval, including depression.