Do I need chemicals if I drain my hot tub after 3 days?
Fill it on Friday, and use it all weekend. On Monday you chlorinate it, and let it sit chlorinated all week. This will prevent bacterial growth from taking over your filter. Drain and refill on Friday before the weekend, and don't add chlorine. Once you're done using it for the weekend, add chlorine. Rinse and repeat next Friday before the weekend. 

I assume your intentions are to not bathe in chlorine, but hopefully the use of it is acceptable to you for spa maintenance during the week when you're not using it. The small amount left over after a drain and fill is negligible, but you could even drain, partial fill, and drain again if you want to be sure. It'll definitely be less PPM of chlorine than is in city water out of the faucet, but you said that water was free, so you may be speaking about well, rain, or lake water. 

If you decide to never treat the water after using it for the weekend, then remove the paper water filter from the water filter housing and replace with either nothing or a perforated metal filter instead. Without any biological control, bacterial will use a paper water filter as a petri dish and grow wild.