Not much to add to the others. I've understood it to mean "endure your own fate." Here are two salient entries from James A. C. Stevenson's Dictionary of Scots Words & Phrases In Current Use (Athlone Press Ltd., London, 1989):

WEIRD: Fate, destiny. Not often heard nowadays, though you may still be told that you have to 'dree your weird', put up with your lot. The word has however won a place in the standard English vocabulary in rather curious circumstances. The Fates, the three classical goddesses who presided over men's destinies, were known in older Scots as the "weirds" or "weird sisters." From the 15th century on Scots writers repeated a legend that the Fates, or "weird sisters," had appeared to Macbeth to lure him to his fate. The story was taken over by Holinshed, the English chronicler to whom Shakespeare went for the plot of Macbeth. Later, people came to believe that the "weird" in the "weird sisters" in Macbeth meant supernatural or uncanny. This misunderstanding gave "weird" its main modern meaning in English. "Weird" was first recorded in Scots in 1375. It is from the Old English word for fate.

DREE: To suffer, endure (pain, misfortune). General Scots, also found in northern English dialect. Someone in a difficult situation for which there is no immediate remedy is likely to be told, 'You'll just have to dree it.' A common form of 'Job's comfort' is "You have to dree your weird', you must put up with what seems to be your fate. Dree has been recorded in Scots since the 14th century. It is from the Old English word for 'to endure,' and has a common origin with "dreich," which is said of things that are hard to bear.

--Cuilionn