This question could get into the realm of needing to be talked about on a physics forum...
Also I am going to speculate as to your specific answers as I'm not totally sure but...
To keep it simple heavier tires will cause slower acceleration from a stop. You are adding unsprung weight. Adding unsprung weight will decrease acceleration when talking about tires and wheels due to rotating mass. Example: a car that weighs 2500 lbs and has 100lbs in wheels and tires will accelerate quicker than a 2500 lb car with 300lbs in wheels and tires.
As far as gear hunting on the highway I think both weight and size potentially could effect gear hunting. I believe the weight could potentially cause more gear hunting but that's just a guess.
Here's why I think that: Gear hunting is the transmission shifting from say 5-6-5-6-5 etc. your throttle input, vehicle speed, load, RPMS, all effect transmission shifting. A transmission shifts up when governor pressure ( vehicle speed ) exceeds throttle pressure within the transmission. A transmission downshifts when throttle pressure exceeds governor pressure. By adding heavier tires OR taller tires you could be changing the internal pressures of the transmission or the input signals that the trans receives. Hydraulic transmissions are no longer made in the U.S. but the theory is generally the same but now done using electric shift solenoids that GET INPUTS FROM THE ECU ( engine computer ). Mainline pressure also plays a roll as mainline pressure is build up by the transmission pump which is RPM controlled. Mainline pressure is the source pressure for the whole transmission including the valve body, torque converter and all clutches. Toyota likes to use an electronically controlled 1/2 lock of the torque converter that's dependent of many factors and inputs but seems generally pressure controlled for the most part. Adding heavier or larger tires could also effect these inputs or pressures.