You are
a sponge.
I grow by consuming one thing
Water.
The more I consume the larger I get
As a sponge becomes saturated, it gets heavier.
Regardless of my size you don't see more of me
Regardless of the amount of water, the amount of sponge material remains the same.
I am lighter than what I consume
A dry sponge is lighter than the same amount of water.
I am something real, something tangible that you can put your hands on, something that can become quite heavy.
Well indeed.
Previous answer
Are you
a balloon?
I grow by consuming one thing
A balloon consumes gas to become larger.
The more I consume the larger I get
Clearly.
Regardless of my size you don't see more of me
No matter how large it gets, there's still the same amount of balloon material, just stretched thinner and wider.
I am lighter than what I consume
Depends what kind of gas you put into it.