Potions and scrolls have effectively no weight

In Pathfinder's antecedent Dungeons and Dragons 3.5, ink or potion vial (Player's Handbook 128) costs 1 gp and weighs 1/10 lb.¹ However, Pathfinder eliminated vial bookkeeping. The DM may still have 16 potions weigh 1 lb. Ask before loading up.

Scrolls in both games possess negligible weight, but a DM may house rule penalties upon a scroll user without at least a scroll case who carries a scroll mountain (or, more likely, upon a scroll user who attempts to locate in the heat of battle a particular scroll from hundreds carried).

¹ In D&D 3.5 the ink or potion vial description says, "A vial holds 1 ounce of liquid. The stoppered container usually is no more than 1 inch wide and 3 inches high" (ibid. and emphases mine). However, on Physical Description says

A typical potion or oil consists of 1 ounce of liquid held in a ceramic or glass vial fitted with a tight stopper. The stoppered container is usually no more than 1 inch wide and 2 inches high. The vial has AC 13, 1 hit point, hardness 1, and a break DC of 12. Vials hold 1 ounce of liquid. (Dungeon Master's Guide 229 and emphases mine)

Pathfinder eliminates this contradiction by omitting dimensions from the vial so that only the physical description of potions and oils includes dimensions.

There's a factor you missed out on: the square-cube law. As Wikipedia describes it:

When an object undergoes a proportional increase in size, its new surface area is proportional to the square of the multiplier and its new volume is proportional to the cube of the multiplier.

Let's consider the implications of this for a moment with a cube of water: it will be one centimeter along each side, and will weigh one gram.

By your math, if you want a cube of water that's ten times bigger, you also just times the weight by 10, for a final weight of 10 grams. But that's just ten times the water, and I think we'll agree there's a big difference between ten spiders and a ten times taller spider. What you probably mean by 'ten times bigger' is a cube that's ten times bigger along each dimension. That gives us a 10 × 10 × 10 cm cube of water.

We'll see what the square-cube law has to say about increasing each dimension by 10, using that 10 as our size multiplier:

• The surface of one side goes from 1 square centimetre to 100 square centimetres. That means the cube's total surface area goes from 6cm² to 600cm². This surface area got increased by the square of the multiplier, 100.
• The volume of the cube goes from 1cm³ to 1,000cm³ (10 × 10 × 10cm). This volume got increased by the cube of the multiplier, 1000.
• Since the weight of water is 1 gram per cubic centimetre, this now weighs 1,000g, or a kilogram.

Applying this to a spider

Let's assume the spider's anatomy remains identical as it gets proportionately bigger, and that an increase in volume leads to an exactly proportional increase in weight. (In reality, an enormous spider would need to have much sturdier anatomy, better breathing systems, and other stuff in order to be able to avoid suffocating and its own exoskeleton caving in on it, but they might not know that. Let's assume imaginary radiation magic is helping here.)

Original: 5.3 ounces at 12 inches.

Multiplication factor: 10, for going from 1 foot across to 10 feet across.

New weight: 5.3 × 10³ = 5.3 × 1,000 = 5,300 ounces = 331 pounds.

This is about the weight of a very young elephant (they're ~200 pounds when born). The large entry suggests creatures this big should weigh at least 500 pounds, so either this is spider is a near-the-mark outlier, or large spiders have actually developed much sturdier, denser, stronger anatomy for their size and thus weigh a lot more. Imagining an enormous spider with more elephantine body/leg proportions is awesome and terrifying for me.

Enjoy your new spider!