How does a "Weak dollar" have anything at all to do with the price of oil?
I would say it has something to do with most of our oil being imported. A weak dollar makes all imports more expensive.
Additionally, most oil on the global market is priced in dollars, yet producers tend to buy things in other currencies like the euro. Perhaps you can see how that upsets oil producers. OPEC and others tend to hold back supply when the dollar is weak. That was true in the 1970's and that's true now.