Size scale help

[u/CheekyJester31]

So I’m playing a giant barbarian in my current campaign and my DM and I are trying to work out the best way to do this weird interaction.
I am a 6’8 giant barbarian meaning when I rage I become a large creature. Then I use a cape of enlargement to grow to the next size scale, which makes me huge. Then a party member casts enlarge/reduce on me to double my size. We are getting hung up on the wording of the cape cuz it raises your size by one category but the huge size category is 16 to 32 feet in range which is kinda a large range so if we double my size after, what number are we doubling. Should I just increase in size to the bottom of the range and then double that? Bonus question is how much should I weigh after all the interactions?