Anchor tackle is not about the weight of the anchor and the size of the chain, but rather about matching all the parts of the system together.
None of us will ever have chain strong enough to hold the boat when the chain is direct from the anchor to the roller on the boat. It will just never happen.
The catenary in the chain is the major function of the chain and to back that up we use snub lines made of an elastic material such as three strand nylon.
So, you have basically bought a huge anchor you expect to hold the boat, but you do not have the chain to work in company with it. If you had bought a 65# anchor (or so) that would work well with 3/8" BBB chain, but with an 85# anchor you really should be using 1/2" BBB chain. All that is way over kill on your boat but the big anchor with small chain is a mismatch, too.
Since the 1/2" is not going to happen, go ahead and get the 3/8"BBB chain. For heaven's sake, do not let folks talk you into expensive hi test chain as even that will never be strong enough to hold your boat if the chain is straight from the anchor to the boat. Make up a couple of 25' to 30' snub lines with 3/4" three strand nylon, a thimble in an eye splice, shackle, chafe gear (I prefer old [free] fire hose from a fire station) and regular old chain hook, not some fancy, expensive set up from the yachting suppliers.
I have anchored through numerous hurricanes and cyclones over my 5 decades as a professional seafarer and have never lost a boat because my anchor tackle failed.