Perhaps the solution for balancing is to determine what an acceptable TU value is for an average weighted soldier and work backwards.
Given a soldier with their weapon and one extra clip, 1kg in additional equipment (grenades, IR goggles, etc) and armor, the average for a soldier with combat armor is about 15kg, 20kg for Nano armor, and 23 for Power armor. 20kg is a good round number for a baseline. The average soldier should fall in the middle of the 0 penalty range of 20%-50% weight capacity, which would put the strength range between 40 and 100, with 40 putting them at the 50% penalty, and 100 putting them at the 20% threshold. Keep in mind that the min/max weight range for a reasonably equipped soldier is 9.7 (plasma pistol and Combat armor) to about 30 (RPG or Bolter) A minimum strength for a plasma pistol drone would be about 20 (at 50% strength threshold). For the top end (Bolter with Power Armor), minimum 60 strength to stay under the 50% threshold. A Plasma Pistol drone would need at least a strength of 50 to ever be under the 20% threshold and get the TU bonus. Recruits are currently spawned with a strength of 30-40. At 40 strength, RPGs and Bolters are over the limit even with Combat armor, and about half of the weapons will incur a penalty with Nano armor. This is not counting extra weight for sidearms, medkits, stun weapons, etc.
Given this, recruits should probably spawn at more like 40-55 strength and be able to gain at least 20 more with experience.
You could also move the threshold to more like 65% to alleviate the need for high strength values.
Of course, I don't know what that does to TU calculations.