I do not recommend you use plastic of any sort, especially not black plastic, unless you are intending to deprive the soil and the essential microorganisms that keep it fertile and healthy within it of light, air and moisture, particularly as you presumably want fertile, healthy soil if you decide to turn it over to agricultural use. The only time to use black plastic is when you are not able to work the land for a while, nothing you want is growing in it and you want to kill off the roots of pernicious weeds or simply prevent growth of any kind, so if that's what you want to do, then by all means use black plastic.
Just pull up what weeds there are to check whether they have grown in the gravel on top - this does not usually occur for 2 or 3 years after the gravel has been spread. You don't say what weeds are growing, but there are some weeds which will happily punch through tarmac and concrete to grow, so weed barrier would not be effective for that type of weed. What type of weedkiller you can relatively safely use would depend on which weeds are growing.