(I'm not sure exactly what TARE stands for, but basically it means that they take off the weight of the container.)
It doesn't stand for anything, it's a word that means the weight of a container without whatever goes in it. From the Oxford English Dictionary:
"The weight of the wrapping, receptacle, or conveyance containing goods, which is deducted from the gross in order to ascertain the net weight; hence, a deduction made from the gross weight to allow for this; also (esp. as tare weight), the weight of a motor vehicle or aircraft without its fuel and other equipment.
Etymology: < French tare (15th cent. in Hatzfeld & Darmesteter) waste or deterioration in goods, deficiency, imperfection, also as in English, = medieval Latin tara, Italian tara, Provençal tara, Spanish tara, Portuguese tara, Old Spanish atara (Littré), < Arabic ṭarḥah that which is thrown away, < ṭaraḥa to reject."
Anyways, that's my solution. Mesh bags for produce, and jars and tupperwares for bulk goods and all the little stuff that falls through.