Weightless is not mass-less.
A ship in space is "weightless" but still has mass.
And even "weightless" is something of an illusion - there is still micro-gravity, even in the middle of the most empty void of the universe.
But that much aside... Keep in mind that the Class (1, 2, 3, 4, 5, etc) represents the amount of space a particular item takes up.
So the 1A Life Support with 1.3 Tons of Mass might occupy 10 cubit feet of space.
The 5A Life Support at 20 Tons of Mass might occupy 50 cubit feet of space, thus justifying its additional mass.
And Life Support is not simply the air supply in your suit.
It's CO2 scrubbers, heating, cooling, and quite a few systems required to sustain human life inside a craft.
Think of it like the air conditioner/furnace in a house. The larger the house, the larger an AC unit and furnace required to heat and cool.
The larger the ship, the larger the unit required to maintain breathable air and to keep you from freezing to death or having a heat stroke.
This also means more duct work to air from the unit to the various parts of the ship, thus more mass for larger units.
The same can be said for Sensors, Shield Generators, and so on - higher Class units are larger units for larger craft, and will require more mass.
As to the why behind sensors... logic begins to break down a bit here... yes, a larger ship may require more sensor nodes to provide the same kinds of detection that a smaller craft can get with fewer, and may require larger nodes as well for the same reasons, but it gets a little stretchy here. If you think about sensors like Wireless access points, it becomes obvious that a ship like a Sidewinder might only need one node to do all its scanning, while something like a Cutter or Anaconda would require many more to provide the same "coverage".
In terms of structures, a single wireless AP might be enough for a small house, while a mansion may require a dozen or more to cover the area.
So there is some sense to it beyond "balance".
Some.