Click the triangle next to "Other Computers". (Or if you're using Arq 3, hover your mouse over "Other Backup Sets" and click the "Show" link). There you'll find your old backup data. Select it and click the "Adopt This Backup Set". This will cause Arq to adopt the settings and backup data it was using on your old computer, so you don't have to re-upload.
(I'm the creator of Arq)