I use TH69 bonded nylon. It's highly durable and the tensile strength of a single stitch > 10 lbs. It however is not super easy to find and is only avaialble by the pound or half pound. However, it'll last a long time and is well worth the investment.
You could probably use Th48 or whatever is a thinner variant and be just fine. 69 doesn't run through most machines without significant tension adjustments.
Most of your local shops will not have bonded nylon in stock, but may be able to order it for you. Barring that, there are many places that sell it online.
If you want a tiny bit to play with, my company sells pre-wound bobbins of it for hand repairs of our goods. The pre-wound bobbins are of course a bit stiffer since they have a tacky spray on them to keep the bobbin together. They don't run super well through non-industrial machines but they work well for handsewing. These are also 100% the same bobbins that Adventure Medical includes in their survival kit.
On the plus side, it's only $.50 per bobbin and is more than enough to do ten-20 packs worth of pack straps. If you do get one from the above link, know that we adjust the shipping down to whatever is cheapest - our site doesn't work well with very light items so we just have to manually adjust shipping rates.