Most information on older trailers typically has vaporized, most had a plastic sticker on the side of the trailer which would have stated the tire size, GVWR and such..
Those stickers over time peeled, cracked, faded until nothing is left.
You WILL have to look sub 15 ft size and SINGLE AXLE to get to the weight you are seeking.
A good hint to figure out the MAX weight of the trailer is to look at the axle/rim/drum.
2,000-2,500 lb axles tend to use 14" tires and the drum/rim will be a 4 bolt hole configuration.
3,000-3,500 lb axles can use 14" or 15" tires but the drum/rim will have FIVE bolt holes.
Keeping in mind that there a couple of exceptions you might run into which are obsolete drum/rims which are often called "star" rims, these have a very large center opening and the bolt holes are rather close to the tire away from the center of the rim.
Star rims are hard to read because you can have 14" or 15" on a lighter axle..
Alternately, take a look UNDER the trailer at the axles, there SHOULD be a aluminum metal band on one the sides of the axle. This band WILL contain the name of the axle manufacturer AND the max GVWR of the axle.
Those bands may or may not be still in tact.
For my 1981 TT, both axles had the bands still attached.
You could check the tire specifications to see what the max GVWR is for each tire, that can give you a hint provided that the owner put the CORRECT tire with the CORRECT weight rating for the trailer.
Some states like PA, ALL the information you seek IS clearly put on the TITLE and yearly registration card, many states, however do not.
If you can determine the max GVWR of the axle, you can then add tongue weight to the mix, tongue weight NEEDS to be 10%-15% of the weight on the axles.
With a single axle, I would HIGHLY recommend 15%, less than that can get squirmy in the handling department.
Dual axle trailers tend to trailer much better than single axle trailers.
Not sure as to why you want such an old trailer, you do realize that 30+ old trailers tend to be built a bit heavier and they WILL need a lot of repairs from hidden water damage..
Hope you are extremely handy with power tools, they WILL be your friends..