This guide uses some short-hand to make things easier.
Weights are given in terms of the equivalent weight of a ballast block set to a certain number. The equivalent weight will be denoted as, for example, '0.50x B' for a ballast block set to 0.50x weight.

Other points of interest will be noted under an item's weight if it is something not immediately obvious (like cannons firing when heated, but not propellors giving thrust when spun.)

Sections will be divided by their categories in the lower bar of the game, i.e., Blocks, Mechanical, etc.

WORKSHOP LINK TO SCALES USED (Marvel at their primitiveness) -
http://steamproxy.net/sharedfiles/filedetails/?id=483001116

STARTING BLOCK - 0.26x B
(caveat: A slightly different set of scales was used for this one, as my original had the starting block in the centre. This number represents the tipping point where it would fall either way. From this point on, each item is weighed using the same standardised scale which has been shown to be accurate via measurement of a ballast on either side set to the same number causing either a lack of fall or for the scale to fall to either side without any clear bias.)

Small Wooden Block - 0.3x B

Wooden Block - 0.5x B
(For clarification, 2 small blocks will weigh more than a regular wooden block even when stacked so they graphically appear as wooden blocks.)

Halved Wooden Block - 0.5x B
(This is the part you get when you try and place a Wooden Block in a space where only a Small Wooden Block would fit. It appears to be identical otherwise to the normal Wooden Block, except for size and shape.)

Wooden Pole - 0.5x B

Halved Wooden Pole - 0.5x B
(This is a half-length wooden pole made using a method similar to the halved wooden block. Thank you to Phantom329 for pointing this one out.)

Brace - 0.5x B
(This figure holds true no matter the length.)

Wooden Panel - 0.3x B - OFF

Hinge - 0.5x B

Swivel Joint - 0.5x B

Ball Joint - 0.5x B

Half-Pipe - 1.0x B

Pin - Weightless
(Tested for the sake of consistency)

Motor Wheel - 1.0x B
(Unpowered and Powered weigh the same.)

Large Wheel - 1.0x B
(Unpowered and Powered weigh the same.)

Small Wheel - 0.5x B

Medium Cog - 0.5x B
(Powered and unpowered are the same.)

Unpowered Large Cog - 0.5x B
(Huh. Light.)

Steering Hinge - 1.0x B

Steering (block) - 1.0x B

Decoupler - 0.5x B

Spring - ~0.35x B
(This one wouldn't behave. The slightest change in configuration threw off my scales, but I'm fairly certain length does not affect weight.)

Suspension - 0.5x B

Slider - 0.5x B

Piston - 0.5x B

Spinning Block - 1.0x B
(Spin speed was set to 0.00x to ensure stability.)

Grabber - 0.5x B

Rope+Winch - 1.0x B
(Regardless of length, like springs and braces.)

Spike Ball - 1.0x B

Metal Blade - 0.3x B

Circular Saw - 1.0x B
(Spinning had little effect on measurement, but higher speeds will cause disruptions.)

Drill - 1.0x B
(Spinning had a more drastic effect than above, but still small.)

Metal Spike - 0.3x B

Cannon - 1.5x B
Fires when heated.

Shrapnel Cannon - 1.5x B
Fires when heated.

Flamethrower - 0.3x B

Small Torch - 1.0x B
Water will put out the flame, more fire will re-ignite it.

Bomb - 0.5x B
Explodes when heated.

Remote Grenade - 0.5x B
Explodes when heated.

Rocket - 0.2x B
These are pretty light! They fire when heated. Explosive charge does not affect weight.

Flaming Ball - 0.5x B
Water will put out the flame, more fire will re-ignite it.

Boulder - 5.0x B

Holder - 0.5x B

Water Cannon - 1.5x B
Fires steam when heated, greatly increasing its thrust.
Puts out fires, regardless of water or steam.

Crossbow - 0.5x B
Because the model is off-centre, it seems it has slightly more weight on the front, where the arrow is. When I measured with the arrow pointing towards the ballast on my scales, it measured at 0.49x B, so it's a very small amount.
Arrows that pass through fire can themselves burst into flame, which can in turn set objects on fire on the other end. Couldn't find a consistent setup with a small torch, but I'm sure you guys can come up with something better.

Vacuum Block - 0.5x B
Like lots of weapons, it's heavier on one side due to being slightly offset from its mount. It's slightly heavier on the 'pump' side.
Can be heated, but I couldn't tell if this changes its function at all. The vacuum effect itself will put out fires.

Flying Block - 0.3x B

Small Propellor - 0.3x B

Propellor - 0.3x B

Wing - 0.3x B

Wing Panel - 0.5x B

Balloon - -0.5xB
(Measured with the balloon set to 1.0x bouyancy)

(Short) Metal Plate - 0.25x B

(Long) Metal Plate - 0.25x B

(Round) Metal Plate - 0.5x B

Plow - 1.0x