Or get four scales, put one under each leg of your table and climb aboard.
I’m a big guy, so I get on my hands and knees and use four scales to take my weight.
Not really. But it’ll work fine if you are okay with four measurements being accurate within a few pounds each.
Good enough for government work. On a physics paper you would have to consider all the tolerances and deal with them statistically in addition to adding all the weights. There might be many things like tilt and other accelerations one can ignore. Most tables are not hugely asymmetrical.
A bit cumbersome, but I just thought of this:
- Put a bottle jack on a scale.
- Cut a piece of 4X4 lumber so that it fits between the bottle jack and underside of the table.
- Weigh the bottle jack and 4X4. Note the weight or tare the scale.
- Put scale + bottle jack + 4X4 under center of table.
- Get two people. Place them at opposite corners of the table.
- A third person uses the bottle jack to raise the table 1 inch off the ground, while the other two people keep the table steady.
- Take reading. Subtract bottle jack and 4X4 weight (if scale wasn’t tared).
This, of course, assumes the table won’t be damaged by lifting it in the center using a 4X4. If there’s a concern about this, you could spread the load by attaching a couple of horizontal 2X4s to the 4X4, and use a couple of diagonal 2X4’s to support the ends.
You don’t need the extra people for that. The only way it works is if the table is balanced, but if it’s balanced, then you need to apply barely any additional force. Regardless, you’d need to go through a couple of iterations to find the actual center of mass.
True, if it’s perfectly centered.
Got to thinking… could also use a floor jack. Stick the scale on the floor jack, then stick the 4X4 between the scale and center of table.
First we must assume a spherical cow in a vacuum…
If it’s not centered–or rather, the support point isn’t directly under the center of mass–then the results will be inaccurate anyway. One of the helpers will have to lift or push down on their side of the table, and that force would have to be added to the reading. So it should be assumed that table has been centered and that it only takes a small effort to position the table at a neutral point.
There was an Archie Bunker All In The Family episode like this in the early 1970’s. Archie got all upset about his weight, so his wife kept turning the scale down so he would weight the same. He weighed the laundry on the scale, then burned out the laundromat washer because he put way too much weight of clothes in it… 
Simpler yet is to put the scale under the table and stand on it while you pick the table up using a modified backlift. Just place your hands on your knees rather than a platform to keep all the weight on your feet, it’s easy to find the balance point for a table and the relative weight would be no problem for anyone to lift.
Easier yet: rather than jury-rigging some sort of supports for the four legs to enable weighing with one central scale, simply turn the table over on its back. It already has a nice solid structure connecting the 4 legs. It’s called the “tabletop”.
You’re welcome! 
Still easier, find the table manufacturer online and see what they say the table weighs.
No, by far the easiest method is to measure the length of every edge of the table, calculate the volume, look up the density value for the wood, calculate the mass, and then calculate the weight.
When I have had this problem, I have simply immersed the table in water, calculated the volume displaced, cut off a piece of table and found its density, and assumed the table is of uniform density.
Even easier – assuming the table is mostly wood, it will float. So simply put in a large calibrated cylinder and see how much the water rises. The apparent increase in the volume of water will match in weight the value of the table. Look up the density of water.
Why yes, I am old enough to have known Archimedes.
(I was joking and just wanted to make the process cumbersome. Eureka!)
Even easier, find a nearby physics student and say “I have this nice scale which you may have if you can use it to tell me the weight of this large table.”
Assume a spherical table.
Ignore friction.
Clearly wrong 
Years back, we had a mechanical scale (versus our current one which is electronic). I once gained (or lost? I forget which) 20 or 30 pounds over breakfast. I think I lost (or gained) the full 20-30 pounds just by the act of stepping off and back onto it.
The new one seems to be more consistent in its readings.
As far as weighing with only one scale: there’s no good way to tell how much of the table’s weight is being handled by the other legs (the ones you aren’t lifting off the ground) - then when you go around to the other end. ditto. I think you really need to isolate the entire table from having any weight supported by anything other than scales.
If anyone has 2 (or more) bathroom scales, science demands that you give this a try ASAP. The “put one foot on each scale” would be a faster proof-of-concept.
Likely the most accurate weight would be to get a big-ass piece of plywood, set that on the scale, and put the table on the plywood.
Then weigh just the plywood separately and subtract that from the first reading.
Don’t give the student too much leeway. Otherwise they’ll just tell you it weighs 100 kg. It’s obviously much more than 10 kg and much less than 1000 kg; therefore it must be 100 kg.