Answer: While I don't think I would describe the stems of this type of hydrangea as particularly stiff and "woody" either, and while this type of hydrangea (H. arborescens) is known to be a bit straggly and floppy and the species does tend to drag its flowers, yours do sound unusually weak for the named variety "Annabelle". There are several possible reasons for why the plants are bending but the most common would be overfertilizng with nitrogen and lack of water. These plants really prefer a moist soil although they will tolerate drier conditions when planted in a bit of shade. Your plants might also prefer a bit more light -- stretching for light can also cause weaker stems. These particular hydrangeas bloom on new wood of the season and so should be trimmed back hard in late winter; this may help add some support to the current year's stems.
Unfortunately this type of hydrangea tends to have generally ratty looking foliage by the end of the season; adequate water and moderate fertilizing should keep it in pretty good shape but it is subject to a wide variety of occasional problems ranging from various pests to mildew and rust. You might want to take a sample to your County Extension (231-7890) for a specific diagnosis and suggested controls.
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