It's actually 1.15... x 10^23 or...
115,848,153,000,000,000,000,000 kilograms
That's 115 sextillion kilograms (I may have mathed wrong but I think this is closer? It's using NBT data and the assumption of 32 maximum layers of it)
The maximum weight you can carry in Minecraft is complicated. For starters, ice is better than anything else because the max amount of blocks one water can make is ~537 million blocks^, and ice stacks to 64. Then you use shulkers and stuff. A cubic meter of water is ~1000 KG, so the max weight Steve can carry in two hands is...
45,778,176,000,000,000 kilograms (45 quadrillion kilograms)
- ^ Citation: Alexa real on YouTube*
comments (single view)
The melted ice thing might win out but I thought it was too much of a stretch, considering that most of the water are not source blocks, not full flowing blocks, and there are not enough blocks in a Minecraft world for all of it.