Chief - I'm curious about your 6 lb./4 oz. RBL 16.
The 29" barrels of my RBL 16 are quite light at 2 lbs./12.5 oz., and the splinter forend is 9.5 oz. The frame is short and compact, the buttstock unnecessarily thick and heavy. Wrist circumference on mine is 4-3/4", and butt dimensions are 5" x 1-5/8". What stock dimensions do you have? I expect you have the buttplate, and likely the shorter 14-1/4" LOP?
I had them fit a thin Galazan pad which I'm currently using instead of the buttplate. This gets mine to 15" LOP and adds nearly 2 oz. net of weight - with the buttplate mine's a shade over 6 lbs. 8 oz. I could take more wood out of the butt to reduce weight and move the balance forward, but I like it as is. My hands aren't small, the thick wrist is comfortable for carrying with one hand while the other is parting cover or on the whistle to turn or stop my dog. And the comb thickness is nice on the cheek for shooting clay targets. Tradeoff is I did need to bend the stock for some cast off.
Jay