There is little difference between a weeks camping tour and a longer one. You still seem to end up taking all the stuff you need.
If you are in a group, it helps to share things, and use the biggest tent you can. Big tents have a better volume/weight ratio than smaller models, eg 2 3-person tents instead of 3 2-person tents.
Do you need to cook ? Save a lot of weight and hassle by eating uncooked food, and getting your main meals at restaraunts. Unlike foot travellers, you can easily travel 5 miles for a meal in the evening.

Before you go, pack everything you think you are going to need in your bags. Test it out in the back garden, sleeping in the tents, using your kit. Try a few bike rides with loaded bikes to make sure they are stable. With a full camping load, it helps to spread the load onto front panniers, but for a week, you may be able to make do with rear only.

Check out some of the "ultra-light" camping websites.