I've fished large fish in this situation a lot over the decades and the best advise I can give you to improve your chances of landing these fish is to really apply upward pressure on them while playing them which keeps the fish close to the surface. In order to do that, you often have to extend your entire arm over your head while playing the fish whether you choose to strip them in or play them off the reel. It's definitely more tiring but it works.
Also….if your plan is to play the fish off the reel which most anglers tend to do with larger fish, it's important that you don't give the fish any chance at all to dive down while getting the line off the bottom of the boat onto your reel so keep applying that upward pressure through that process if it arises.
Giving the fish its head back so that it has the upper hand by not applying this upward pressure or by giving the fish any slack at all during the fight will almost certainly end badly because the fish will dive for those weeds. If the fish gets wrapped in tougher, stronger weeds than your tippet material then you have to be damn lucky to be the victor! You'll have to lift anchor, get above the fish, and gently pull upward hoping for the best.
If leader/tippet strength and thickness isn't an issue then by all means, go heavier, but if it means just the odd hookup compared to what you might get? Well, I'd rather take my chances that I'm likely going to lose the odd fish by going lighter. However, because I'm going to get more hookups from lighter tippet material, I'll get to practice this skill mentioned above. Then, hopefully, I'll be the one in control.
It's pretty common sense that large fish don't get that way from being stupid. One reason, besides others why they get that way, is because they notice things like thicker, stronger, more visible leader line and will, in most cases, simply turn their nose up at it so ONLY ever go as heavy as the fishing allows so that your day will not be affected adversely. To me, that's usually 6 lb. tippet material.
Besides…. even if you do lose some fish to the weeds due to lighter tippet material that's a whole lot more fun than fishing with clothe line and not getting any hookups at all! LOL