I've been mainly focusing on AC for my ranger, pretty much all the items he wears he got himself. By level 40 I'm often over 200 str (all from incidental +str on items or on buffs). I don't remember where i put my starting stats, but lets assume i put it all in str; i'd still be at 180 str if I had put those starting points elsewhere.
Basically by mid levels you won't be having problems with low str weighting you down.
In the mean time try stick to low weight food (don't fill your inventory with stacks of that heavy foraged stuff) and take a good look at your items and consider if the weight is worth whatever advantages you get. Often it is worth swapping down a size in armour if you can. Also, some reinforced armour gives the same AC as banded, but weights significantly less. Finally, if you want a set of ~leather stat armour that weighs little (which should be plenty at low levels) consider murdering a bunch of frogloks in guk for Mesh.
If you have a little money, Targishan's bone mask is a 12AC 0.0 weight face and Azure Sleeves are similar stats for arms. Much Ivy Etched armour has a decent amount of pieces with +Str.
In your situation, I suggest you ideally want to go with items that have more strength than weight and plenty of hp/ac (as much as possible).
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