Below is an email from Tom Lathrop, designer and builder of "Liz", explaining how to weigh a boat while on the trailer using only a bathroom scale.
 

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Ray,

Here is the method I use to weigh boats on a trailer without hauling the boat to a commercial scale, which requires two trips for boat and trailer.

It's simple, accurate and will cause bystanders to marvel at your engineering whiz.

The boat stays on the trailer the entire time. Put the scale under the tongue near the end. You can even put a block on the scale to lift the tongue so you can see the dial. Record the weight. Now, slide the boat aft on the trailer 12" to 18". You must measure exactly how many inches you moved it, and record that. With the scale in the same location under the tongue, record the new scale reading. Finally, measure the distance in inches between the trailer axle (wheel centerline) and the point on the tongue where it touches the scale. You have then four measurements:

W1 = first (heavier) scale reading in lbs, W2 = second scale reading in lbs, X = the distance you shifted the boat in inches, C = distance between trailer axle and scale point in inches.

The formula is Boat Weight = C (W1-W2)/X

A couple of notes. The result, like any measurement, is sensitive to the accuracy of the input data. In this case, the most critical is the distance you slide the boat. One inch error out of 12 inches will really make a difference in the result. Slide the boat as far as you can and still have a readable load on the scales. Notice, too, that by subtracting the two scale readings, any constant error in the scale is canceled out.

Note to techies: The formula was derived by taking the sum of the moments around the trailer axle for each case and (since the sum of moments about a stationary object is zero) set the two equations equal to each other and solve for the trailer weight. Things that you don't know, like the trailer's weight and the location of the boat's center of gravity cancel out, leaving just the variables that you can measure, and the boat weight.

I also use another version of this formula for weighing a boat while it is under construction so I don't get a bad surprise when it's finished. You can use two bridged scales and/or a trailer extension to increase the range of weights you can measure. I usually shoot for measurements of about 30-40lbs
for a low end and 250lbs or so for the high end. 

In your case I would reverse the order of moving the boat and do it when you next go to the launch ramp so you can move the boat in a partial launch.

Tom Lathrop

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The easiest way for me to accomplish this was take the bathroom scale and  tape measure to the ramp.  When I pulled the CS out I allowed it to stay aft on the trailer held in place by the bow wench line.  Once on the parking lot I cut the trailer loose from the truck and weighed the tongue.  I then measured the distance from the transom to the end of one of the bunks. Now I pulled it forward with the wench.  I measured the difference in posistion and re-weighed the tongue.