Most hydrangeas get thicker, sturdier stems with maturity. If your plant is less than two years old - Give it some time and it will get stronger. If you have it planted in full shade the stems will tend to stretch and be flimsy. A sunnier location will solve the problem. Avoid excess water and fertilizer as this will lead to weak stems. Also prune out about a third of the weakest stems so the remaining stems get more energy and are better equiped to hold the flowers. Good luck.

hoosier and duncan, thank you, thank you for starting this question and for the very helpful answer. I had the same exact question. I hate seeing all the stems on the ground, knowing I can't cut them all. Because my Nikko BLue hasn't bloomed for a couple of years, I overfertilized it this summer! And my Blushing Brides and Big Daddys and Forevers are all dragging.
Thanks you "guys" again.
Pat
Ypsilanti/Ann Arbor, Michigan (no offence, Duncan!)