As cockerels go through puberty the hormones both add flavor and texture to the meat. Some of us like that extra flavor, others call it gamey and do not like it. Added texture means it can get tougher or stringier. Again, that bothers some people more than others. Some of that is what you are used to and some is just your personal preferences.
There are three different methods of treating the meat after butcher. One is "aging". If you cook any chicken when rigor mortis has set up the meat is going to be tough, it can be inedible. So you need to age it until rigor mortis has passed. You'll see all kinds of charts and tables as to how long it needs to age, I ignore them. If the joint moves freely rigor has passed. That might be 24 hours, it might be 36 hours or more. You need to keep the meat cold so bacteria doesn't grow while aging. That might be your fridge or an ice chest. It might be wet in ice water or dry with just ice or cold. If in your fridge a lot of meat can raise the overall temperature to a dangerous level. You might want to chill it first.
"Brining" means soaking it in salt water. You can add salt flavor at any time. The purpose of brining is that the salt gets it to hold moisture. If you are cooking it with a wet method brining isn't very important. But if you are cooking it dry like grilling or frying then brining can improve the quality of the meat.
"Marinading" is when you use an acid to break down the fiber which lessens toughness. Some popular marinades are based on beer, wine, vinegar, or tomato products. The longer you marinade the more the fiber breaks down. If you marinade too long the meat can get kind of mushy, especially a young bird. But with older birds cooked certain ways marinading can be very important. Some people combine marinading and brining with aging. Lots of different ways to go about it.
How you cook the bird is important and depends on age. A young tender bird can be grilled or fried, a hot fast method. As it ages you need to change cooking methods. Generally this means a lower, slower heat and adding moisture. One exception to this (there are always exceptions) is pressure cooking. A moist method but with high heat. Properly done the meat will be fall off the bone, really tender.
Again you can get charts and tables on what age you can cook a certain way. I don't pay much attention to those. Some cockerels start puberty pretty young, others much later, so they are at varying stages even at the same age. Aging, brining, and marinades have an effect. And we have different preferences. I don't have any great magical method to determine this. Cook one a certain way paying attention to age when butchered. If you like it, great. If you don't, try cooking the next one differently. You will find your sweet spot.
My question is, at what age is it worth the expense of having a rooster processed (I don't really want to do it ourselves). Alternatively, at what weight? But I have no idea what weight they are and haven't yet considered how to get one.
That is a purely personal question. Dual purpose cockerels can vary by age but typically 16 weeks is a sweet spot where the amount of meat is respectable. It is not great but younger than that they are typically more bones than meat. I like to butcher mine at 23 weeks. That suits the way I cook them. That is usually about the end of a growth spurt. They will continue to gain weight after that but the rate of gain is pretty slow. Mine forage for a lot of their food. If you are buying everything they eat then it can get pretty expensive to feed them.
Most of us cannot raise cockerels for meat at a less cost than the meat you can buy at the store. We do not operate at the commercial scale and do not use the special meat birds that they use. Our growth rate is much less. They have the benefit of operating at scale. I do not raise my chickens for meat because of reduced expense. I raise them for my own reasons.
My dilemma arising is they are already starting to crow, and they aren't aggressive yet but I can certainly see it starting.
Yes, puberty can start at different ages and is why some people butcher their cockerels when they start to go after the pullets or fight each other even though they are still mostly skin and bones. As always, that can start at different ages. How rough it is on the pullets or each other can vary a lot each year. Most of the time I can live with it but every three or four years it gets rough enough that I isolate most of my cockerels in a "grow-out pen" with their own coop and run. If they don't have the pullets to fight over it is usually not that rough. In any year, I start eating the trouble makers around 16 weeks, they don't all make it to 23 weeks.
I firmly believe that the more room they have the better they behave. You have much better chances of the cockerels not bothering the pullets to the point they are in danger and you have better chances of fights between the cockerels breaking up before one is killed if they have enough room to run away and stay far away. That's a lot more room than that 4 square feet in the coop and 10 square feet in the run that you keep reading on here. A lot of this will depend on your personal tolerance for cockerels force mating pullets or fighting among themselves.
I don't have any hard and fast rules for every chicken on the planet. There are way too many variables, many of them personal and all of them unique. All I can suggest it to use trial and error to see what works best for you and never be afraid to ask specific questions. On rare occasions I can actually be specific.
