On their site it says it supports DVD-R DL burning but no mention of DVD+R. I don't see many reliable blank DVD-R DL brands in the shops (ie Verbatim) so does the Sony AD-7280S support DVD+ DL recording?
It supports DVD+R9 which is another name for DVD+R DL. So: Yes, it supports DVD+R DL. [It's completely over my head why Sony chose to call one DVD-R DL and the other DVD+R9. DVD-R DL is also called DVD-R9.]
Tip: Install CDBurnerXP, run it and choose "Data disc". In the main window's menu bar, choose "Recorder > Device information" and choose the correct recorder drive letter. It will tell you exactly what your optical media drive is capable of.