Rose can't support its own weight?

Hi all, we moved into a house 2 years ago that has a beautiful rose in the front garden. It's very well established but I think has been subject to some brutal pruning previously. It has really thick woody stems at the base, but then from this the new shoots with flowers on don't seem to have any strength in them so they just fall over each time it flowers. It has been staked up in a couple of places for additional support. Anything I can do periodically to encourage strength in the newer shoots? I have absolutely no idea what type of rose it is. Thank you

 

I've got one rose bush and every year I have to support the flowers.
I just think thats how some roses are, especially when it rains.