Actually some of the roses affected were already here when we moved in. I've amended the soil somewhat by adding alfalfa and banana peelings trying my best to stay organic. On the whole, the roses seem to be enjoying their sunny location and have grown very tall with their main canes being quite sturdy. It's just the smaller stems branching out from those canes that
are having a hard time supporting the large flowers. I just feel there must be something I can do to strengthen these supportive stems to make their task a little easier.

So, as suspected the problem is the production of slender branches. You might try cutting them down lower next Feb. to make it so the plants consist primarily of a small number of canes of large diameter when they grow back, you having also pruned out twiggy side branches at the same time. If you want your Hybrid Teas to look like a cut bouquet of big, up-facing long stem roses stuck in the ground this should help produce that effect.

Otherwise the alfalfa etc. are nutrient sources just as if you were applying chemical fertilizers - you should have some idea what the nutrient balance is in your soil (determined by sampling it and having it analyzed by a soils lab - ask your local Cooperative Extension office about this) before making repeated applications. Rose plantings don't necessarily need high levels of fertility and you can poison any soil with too much of anything. In this area cultivated soils often only require nitrogen supplementation, many products used by people trying to promote flowering or fruiting in particular are significant sources of phosphorus. This is an element that does not leach much, making it hard to get rid of if you go overboard.

Great information to help me work out a new strategy for countering the weak stems issue for my roses. But I do have to be careful not to cut the plants too drastically. Just a few feet in front of my rose bed, facing east, there is 4 ft. wall that will block the sunlight from canes cut too short.

Good heads up about the phosphorus. Perhaps the bonemeal I added last year could have caused an imbalance in the soil. When we first moved here, I had pondered the possibility of going the soil analysis route to help calm my angst about learning about gardening in a very different climate than I was used to. However, my yard is quite huge with variable elevations which seemingly would necessitate tests for quite a few soil samples that could add up to $$$. However, in this case, soil testing on my rose garden soil does make a lot of sense.

http://puyallup.wsu.edu/wp-content/uploads/sites/403/2015/03/bonemeal.pdf

And here I thought I was doing my roses a favor. I appreciate the link and the education that came with it.

More of the same kind of thing from the same source.

http://puyallup.wsu.edu/lcs/

I was on another thread of the same topic. I have a Hybrid Tea (Peaudouce) rose in an exposed area, whose flower stems snap off about 3 to 5" below the rose in any type of wind. The same rose was fine in a less windy spot at my old house. As for thick stems on older shrubs, we don't have that option up here (close to Niagara Falls in Canada). The roses die down in the winter and we have only stubs that start anew every spring. I am moving this shrub to beside a fence to give it some protection from the wind. At least I have a steady supply