An 88# new gen anchor is horribly mismatched with 3/8" chain.
3/8 G7 is stronger than 1/2 G30 or BBB chain and a little weaker than 1/2 G40 HT chain. With G7 chain the normal procedure is for the chain maker to incorporate a larger link on each end. So appropriate strength shackles are not a problem. With G8 shackles you can just get away with a normal sized link in most cases, but it is not expensive to order the chain with the larger links added.
So generally you need not be concerned about a strength mismatch dropping down one chain size at the same time as going from G3 or even G4 chain to G7.
Steve Dashew was one of the pointers of the of the philosophy of adding weight to anchor and reducing the weight to the rode as avway to increase the performance of anchoring equipment and /or save weight.
He uses 3/8 G7 chain with a 240 lb (wow

) Rocna. So an 80lb Manson Supreme with 3/8 G7 is not extreme by any means.
You can read about his anchoring equipment here:
SetSail » Blog Archive » Anchoring System Logic
The Rocna website also suggests there is no mismatch. They actually list thinner 8mm (or 5/16) as the "appropriate" G70 chain to match with a 40kg (88lb) Rocna. The Rocna and Manson Supreme are very similar anchors.
http://kb.rocna.com/kb/Chain
G4 chain is easy and cheap to get. If you have an oversized electric windlass and a boat where the chain weight has little impact it is a good simple choice. If you want to improve your anchoring system without adding more weight. G7 chains are worth considering. The combination of heavier anchor with longer chain (so you can enjoy deeper anchorages and use a longer scope in bad weather) has got appeal.
My ultimate cruiser would incorporate a chain locker well back from the bow with a big anchor winch so lots of standard G4 chain could be carried, but sadly few boats are built this way.
I have some sympathy for those that want to keep things simple and reliable, but I agree that an electric (or hydraulic) anchor winch is almost essential, especially on a larger vessel. The rapid recovery of chain is an important safety feature and the fuss free nature of anchor handling encourages skippers to re-anchor if things are not right.