Inventory space is:
10 Hotbar
40 Inventory
1 Trash
1 Held

4 Ammo
4 Coin

14 dye
6 Armor
12 Accessories (must all be different)
1 Hook
1 Minecart
1 Mount
1 Pet
1 Light Pet

A short bit of searching has revealed that not lead, not gold, but Platinum has the highest density.


Terraria has a little problem in that 4 cm3 of platinum ore does not produce NEARLY 1 cm3 platinum.
Therefore, Terraria's ore must have a higher ore content than usual - and as such we cannot use standard density properties.

4 Plat Ore = 1 Plat Bar.

However, we do know the density of pure platinum. Assuming that the losses of the ore are transferred into the little nicks and decorative corners of the places bars, we can essentially say that 4 plat ore contains 1 part plat and 3 parts stone.

Platinum has a density of 21.45 g / cm3 = 21450 kg / m^3
1 block is 2x2x2 feet ^3 = 8 cubic feet = 0.226534772... m3

This means 1 plat block has mass 4859.170... kg, which is about right for a 2x2x2 feet of solid plat.

So the total platinum weight of the ore he's carrying is 4859.17... x 52 x 999 x 1/4 = 63,573,572.79 kg

(As a side calculation, the mass of a single stack of Platinum ore is 1,671,850 kg. This comes in useful later.)

Now, stone is a HUGE term. It is probably best approximated as just the Earth's crust as we're not getting quite deep enough into the Earth's core to be getting entirely molten rock.
The density of the Earth's crust is 2.7g/cm^3 = 2700 kg / m^3 , and we know the Terraria hero is carrying 52 x 999 x 3/4 blocks of stone ( = 38 961 blocks). One block is 0.226534772 m3, so we know that the Terraria hero is carrying 8826.019 m^3 worth of rock. This means he is carrying 8826.0... x 2700 kg worth of rock = 23,830,251.91 kg of rock.

ARMOR:
Plat Armor is the heaviest followed suit by Gold Armor. One goes in vanity and the other goes in equipment - it doesn't matter.

Gold Armor is made from 90 Gold Bars = 393,899 kg
90 Plat Bars = 437,324.8 kg

Thus the TOTAL MASS OF 52 STACKS OF PLATINUM ORE AND THIS TASTELESS EVENING DRESS IS 87,767,424.01 kg .




COINS:
Platinum stacks up to 999 so is clearly the heaviest choice. Conveniently, platinum coins exist, one of which have a face value of $100 = 100 gold coins. It has a mass of 31.120 g, so four stacks of that to 999 results in 124.35552 kg worth of coin.



ACCESSORIES:
A Minecart has a mass of ~250kg.
The Drill Containment Unit has no real-life counterpart as the rock you are drilling IRL has to go SOMEWHERE and cannot simply drop to the ground in stacks of hundreds.... 10000 kg will do for an industrial drilling vehicle that is one-person and has laser cannons on it.

We are allowed twelve accessories. The heaviest of these are the Diving Helmet, Diving Gear, Jellyfish Diving Gear, Arctic Diving Gear. The weight of these usually hovers around 10kg, so we have 40 kg of Diving accessories.
That is of course four slots. A bit of research has turned out that sizes are far too variable - Totems and Bells are made in all sorts of sizes, so we can safely say 10kg for the remainder of all sorts of faff.


Ammunition is neglegible because of the uncertainties in the DCU.

Of course, the Piggy Bank, Safe, and Defender's Forge all allow you to put MORE items in.... and of course you're still carrying them all. We can essentially say that all of these have 39 slots (as one for storage of the other). Which comes out as 195,606,450.5 kilograms of ore.

A safe that won't blow your house up when you put it down has a mass of roughtly 500 kg. Piggy Banks have a neglible mass and no data can be found for the Forge.

195,606,450.5 kilograms of ore and stone in storage
86,936,200.2 kilograms of ore and stone
437,324.8 kilograms of plat armour
393,899.0 kilograms of gold armour
10,000 kilograms for DCU
500 kilograms for a safe
250 kilograms for a minecart
124.4 kilograms of pocket change
40 kilograms for diving gear
10 kilograms for accessories et al
1 kilogram for Fairy Bell
1 kilogram for Tiki Totem

= 283 384 799 kg with some rounding errors inherent


All hail Chuck Norris!

Hey, Nova here. Aidenpons and I have made a number of assumptions while making our calculation. A major one is that there is no significant loss of platinum while refining the ore. If there is loss, the ore would need to contain more platinum, increasing our hero's strength further. In addition, we've used the average density of the Earth's crust to determine the density of our generic "stone". The ore consists of at least 25% platinum by volume, more if significant losses are present.

There was some guesstimating involved in deciding upon the masses of equipment and non-specified accessories, the latter of which was referred to as "stuff" during the conversation. A kilogram per slot seemed reasonable, given the range of accessories and their masses. The mass of a grapple was ignored, partly because a regular grapple doesn't reach a kilogram while a grapple that can carry millions of kilograms doesn't exist yet. And, like Aidenpons said, the DCU was guesstimated based on a number of details.

All in all, I'm pretty happy with the result. Hope you enjoyed reading about our work.