I did some simple metric calculations, starting with the following measures:

• 125 x 75 x 75 cm, based on 50cm Amah


• The gold was 2cm thick (a finger) for the ark and 10cm thick (a Tefah) for the Kapores, weighing 19.3 g/cm3


• The wooden ark was of the same dimensions 10cm thick and density of 1.2 g/cm3


• The Cherubim were humanoid 100cm high made of gold


• The Luchos were made of sapphire, 60 x 60 x 10cm, 4 g/cm3

I arrived at approximately 4 metric tons.

Are my assumptions and calculations right?

I go through the math here. Admittedly I use a lot of very rough estimation. I caught some mistakes in my math in the video which I have edited here, as well as adding a section below regarding the contents of the Aron.

It's important to note that according to R' Meir, the amos used are 6 tefachim each, while according to R' Yehudah, the amos used are 5 tefachim each. (All sources used to justify these and other numbers later are cited at the bottom.)

Gold

Making these conversions, according to R' Meir:

• The outer gold box was (9.25x9.25x15.25)-(9x9x15)=89.83 cubic tefachim


• The inner gold box was (8.5x8.5x14)-(8.25-8.25x13.75)=75.64 cubic tefachim


• The cover was 1x9x15=135 cubic tefachim


• The crown I assume was one fingerbreadth thick, giving a volume of 2x(0.25x0.25x9)+2x(0.25x0.25x15)=3 cubic tefachim


• The plating of the poles was approximately 2x(3x0.5x0.25)=0.75 cubic tefachim, rounding π=3


• The rings were 4x(3x0.125²)x(2x3x0.625)=0.19 cubic tefachim


• The Keruvim, estimating based on their wingspan covering the entire Aron and scaling a human child's volume down to a height of 10 tefachim, were approximately 2x(0.56x0.56x10)+(0.25x9x15)=40.02 cubic tefachim

All of the above was made of gold, yielding a total of 344.43 cubic tefachim of gold according to R' Meir.

According to R' Yehudah:

• The outer gold box was (7.75x7.75x12.75)-(7.5x7.5x12.5)=62.67 cubic tefachim


• The inner gold box was (7.25x7.25x11.5)-(7x7x11.25)=53.22 cubic tefachim


• The cover was 1x7.5x12.5=93.75 cubic tefachim


• The crown, making the same assumptions, was about 2x(0.25x.025x7.5)+2x(0.25x0.25x12.5)=2.5 cubic tefachim


• The plating of the poles was approximately 2x3x0.5x0.25=0.75 cubic tefachim (same as R' Meir)


• The rings were 4x(3x0.125²)x(2x3x0.625)=0.19 cubic tefachim (same as R' Meir)


• The Keruvim, using the same methodology as by R' Meir, were approximately 2x(0.67x0.67x10)+(0.25x7.5x12.5)=32.42 cubic tefachim

For a total of 245.5 cubic tefachim of gold according to R' Yehudah.

Wood

The poles and middle box were both made of wood.

According to R' Meir:

• The poles were 2x3x.5²x60=90 cubic tefachim


• The middle box was (9x9x15)-(8.5x8.5x14)=203.5 cubic tefachim

Totaling 293.5 cubic tefachim of wood.

According to R' Yehudah:

• The poles were 2x3x.5²x60=90 cubic tefachim (same as R' Meir, as R' Yehudah agrees to a 6-tefach amah for the building, and we derive the length of 10 amos from the building)


• The middle box was (7.5x7.5x12.5)-(7.25x7x25x11.5)=98.66 cubic tefachim

Totaling 188.66 cubic tefachim of wood.

Converting to Metric and the Final Answer

According to Rav Moshe, a cubic tefach is equivalent to 751.83 cubic centimeters. Since the density of gold is 19.32 g/cm³, R' Meir's 344.43 cubic tefachim of gold weighs 5,002.97 kilograms, and R' Yehudah's 245.5 cubic tefachim of gold weighs 3,565.97 kilograms.

The wood used was specifically cedar wood, which has a density of 0.58 g/cm³. R' Meir's 293.5 cubic tefachim of wood weighs 127.98 kilograms, and R' Yehudah's 173.66 cubic tefachim of wood weighs 109.42 kilograms.

Adding these together yields that:

• According to R' Meir, an empty Aron weighed 5,130.1 kilograms.
  


• According to R' Yehudah, an empty Aron weighed 3,675 kilograms.
  

Contents of the Aron

As I noted, I discuss an empty Aron, whereas you include the Luchos in your calculations. The following additions are not discussed in the linked video.

The Aron contained:

• At least one set of Luchos (which were 6x6x3=108 cubic tefachim for each set) made of solid sapphire (3.98g/cm³), yielding 323.49 kilograms each. According to some opinions, the shattered Luchos were also kept inside the Aron, rather than in a separate one, which doubles this number.


• According to R' Meir, a Sefer Torah. (I'll leave its weight as an exercise to the reader; it was 2 tefachim wide by 6 tefachim tall. According to R' Yehudah, it was kept with the Aron, but not in it.)


• According to R' Yehudah, silver rods (two at 1 tefach wide by 7 tefachim long = 5.25 cubic tefachim at 10.49g/cm³ yields 41.41 kilograms)


• A jar of mann, a jar of anointing oil, and Aharon's staff were all placed next to the Aron, so their weights don't count for our purposes.

Conclusion

Four metric tons (=4000 kilograms) isn't a bad estimate...for an empty Aron. For a full one, you're waaaay off.

Sources

• Eruvin 14a-b - justifies π=3


• Bava Basra 14a for most of the numbers mentioned, as well as the dispute between R' Meir and R' Yehudah


• Tosfos to Menachos 98b regarding the rings


• Yoma 72b regarding the nested boxes


• Sukkah 5a-b regarding the cover and the Keruvim