For vehicles an important consideration is its ground pressure, how much force per area (psi or kPa) is being exerted on the ground. The ground can only support so much before the vehicle sinks into the mud. If we can calculate the area of the AT-TE's feet, this can be used to establish an upper limit on the vehicle's mass.
Ground pressure is weight over area. Normally this would be a problem for a space-fairing army as different planets would have different gravities producing different weights (and thus ground pressures) for the same vehicle. A vehicle that worked on the Moon would sink into the ground on the Earth. Fortunately for us, most inhabited bodies in Star Wars have Earth-like gravity. If there's evidence of the AT-TE performing well on high gravity worlds, the mass estimate would be lower.
The AT-TE's feet are a problem. Tracks greatly reduce ground pressure by having a large area relative to the size of the vehicle. An M1 tank has half the ground pressure of a family car despite being 40 times the mass. The AT-TE doesn't have tracks, it has feet. More area than wheels, not as much as tracks.
To make matters worse, the M1A1's ground pressure is fairly constant whether it's moving or standing still. The AT-TE walks (inefficiently) by moving three feet off the ground at a time. All its weight must be supported by its remaining three feet halving its ground area.
What's the area of those feet? Wooykipedia states an AT-TE is 13.2 meters long. To figure this out I scaled up a picture of an AT-TE so that the vehicle is 13 cm long giving a 1 cm = 1 m measurement. I then measured the feet to be 1.5 cm wide giving a diameter of 1.5 meters and a radius of 0.75 meters. I will assume they are circular. Area of a circle is
pi * radius * radius which gives us
3.14 * 0.75 m * 0.75 m and an area of 1.75 sq meters.
Each foot also has four duckbills to increase their effective area. They're a bit harder to measure because of the perspective, I will approximate them as a 0.5m x 0.25m rectangular area giving 0.125 sq meters per duckbill.
So each foot, plus four duckbills, has an approximate area of 2.25 sq meters. Three feet on the ground while walking us 6.75 sq meters of ground area while walking.
I'll use the simple formula for static ground pressure, weight / area. When walking the AT-TE would exert even more. An M1A1 tank has a ground pressure of 103 kPa, excellent off-road performance and a top speed comparable to the AT-TE's 60 kph. 103 kPa is 10,300 kg per sq meter. With 6.75 sq meters to work with we get about 70 metric tons or a bit more than an M1A1 tank.
An adult horse exerts 170 kPa. While this might seem a better analogy to an AT-TE than a tank, they both have legs, a horse and an AT-TE move very differently. But why not, let's use a horse as our upper bound. 170 kPa is about 17,000 kg per sq meter. Since we have 6.75 sq meters to work with, we get an upper bound weight for the AT-TE of 114,750 kg or about 114 metric tons.
Let's run Null's "scaled up M1A1" estimate through the formula. 284,489 kg / 6.75 sq meters is about 42,000 kg per sq meter or 420 kPa. This is roughly the ground pressure for a bicycle which have awful off road performance (ever ride a bike on a beach?). We can state with confidence this estimate is too high. For its volume, the AT-TE must be lighter than a modern tank.
I would say an AT-TE weighs at most 110 metric tons and probably 70 metric tons given its demonstrated off road performance.
PS Somebody check my math. :)