What weight of well finished cattle enjoy the greatest demand on the fat cattle market?

This depends on the year. I have seen the packers want 1250 weight fats and this year I am hearing they are pushing that up close to 1450 on the fats. Taking a guess at the 1200-1300 lb steers.

That's a changing factor Jerry. The feedlot buying my calves has been pushing the weight up.#1300 was about right for a long time, now wanting 1600# steers finished weight.
Lot's of variables there besides that. Sometimes the market for leaner carcasses versus input costs will dictate killing those cattle sooner making lighter weight at slaughter. Breeding also plays a huge role.
I'll say 1350# for my crossbred cattle. Final answer.

Keep in mind that if the numbers to kill are down say 10%, raising the slaughter weight 15% gives the same volume. Most packers would rather people complained about the cuts getting to big than hear the counters are empty.

One thousand pound cattle.

Wes, and KM, you are correct. The answers I have are for 1935. So some of the stuff, such as the today's question, may not be very relevant but more historical.

Exactly Dale. That is the reason given for the larger framed cattle they're wanting now.
The cow and feed it'd take to make such a critter isn't practical for the country I run in.

1000# is actually bigger than I thought they'd use in '35. Interesting.

During the second world war, they wanted little animals packing more fat than big ones. Glycerine for making explosives was worth more than the meat. We used to have a wide range of sizes of stock to fit the envoirement. That was back when slaughter was done without much mechanization. Didn't make much difference what size they were when they was worked in beds instead of on the rail.
Back at about 1900, the average lamb was about 45 lbs. One hundred was the market in 1960, 120 in 1980 and 140 today. Hogs made the same changes.
Before we had fast trucks and the railroad moved a lot of cattle, stock stayed at home until they couldn't be run any longer. That was the day of the grass fat 12-1400 steer. Then is got to be where you moved them a long way between summer and winter range. Now the price of transportation has stopped that.
Read that the cold train hauling produce from Washington to New York got shut down. The oil and coal trains were given priority.