På den ene siden: pris. På den andre siden: vekt.

Because this is a fixed Norwegian pattern for setting up a contrast between two considerations. It works much like on the one hand ... on the other hand in English.

So the sentence is not just listing two random nouns. It is framing them as two competing factors.

Here, ene means one in the sense of the one ... the other ....

So:

• den ene = the one
• den andre = the other

It does not mean the only in this sentence.

This is a very common Norwegian pattern often called double definiteness.

When you have:

• a definite determiner like den
• plus an adjective like ene or andre
• plus a noun

the noun usually also appears in the definite form.

So:

• den ene siden
• den andre siden

Compare:

• den røde bilen = the red car
• det store huset = the big house

So den ene siden is the normal structure.

Because annen changes form depending on the grammar around it.

A useful contrast is:

• en annen side = another side
• den andre siden = the other side

After den + adjective + definite noun, Norwegian uses andre here.

So in this fixed pair, den ene ... den andre ... is the normal form.

Because på den ene siden / på den andre siden is the established idiom.

Literally, it looks like on the one side / on the other side, but in actual use it often means a figurative contrast, not a physical side.

So på is not something you would normally swap out here.

This is an elliptical or note-style structure. Norwegian often leaves out words in headings, slides, bullet points, and short contrastive statements when the missing information is obvious.

So this sentence is more like a compact outline:

• På den ene siden: pris.
• På den andre siden: vekt.

A fuller version could be something like:

• På den ene siden må man tenke på pris. På den andre siden må man tenke på vekt.

The short version sounds natural when you are just naming the two factors.

Because they are being used as bare nouns to name categories or factors, almost like labels.

Here they mean:

• price as a consideration
• weight as a consideration

This is very common in Norwegian, especially in short note-like writing. English does the same in headings and lists.

If you were talking about a specific price or a specific weight, the wording might be more explicit.

The colon introduces the specific item that belongs to each side of the contrast.

So the structure is basically:

• On the one side: price
• On the other side: weight

It gives the sentence a concise, list-like feel. You often see this in presentations, notes, summaries, or argumentative writing.

Not if you want this exact idiomatic contrast.

For the standard on the one hand / on the other hand pattern, Norwegian normally uses:

• på den ene siden
• på den andre siden

Using på en side would usually sound more literal, less idiomatic, or simply unnatural in this context.

Yes, in Bokmål you may also see sida if you use the feminine form of side.

So both of these are possible:

• på den ene siden / på den andre siden
• på den ene sida / på den andre sida

siden is very common, but sida is also correct for speakers who prefer feminine noun forms.

Yes. På den ene siden ... på den andre siden normally sets up a two-part contrast.

It is best when you are balancing one consideration against another. If you want to list many points, Norwegian would usually use a different structure instead of repeating this one.