Ограничение по весу для личного пользования указано в таможенной декларации.

Because the grammatical subject is ограничение (restriction / limit), and that noun is neuter singular.

So the short passive form has to match it:

• указан = masculine singular
• указана = feminine singular
• указано = neuter singular
• указаны = plural

Since ограничение is neuter, Russian uses указано.

It comes from the verb указать (to indicate / to specify / to state), but in this sentence указано is a short passive participle used predicatively.

A natural English equivalent is:

• is indicated
• is stated
• is specified

So the structure is basically:

• Ограничение ... указано ...
• The limit ... is stated ...

This is a very common formal/written Russian pattern.

In this sentence, по весу means by weight or with regard to weight.

The phrase ограничение по весу is a standard way to say:

• weight limit
• restriction based on weight

Here по is used with the dative case, so:

• вес → весу

This pattern is common in Russian:

• ограничение по возрасту = age restriction
• ограничение по времени = time limit
• ограничение по скорости = speed limit

So по + dative often means in terms of / by / with respect to.

Yes, but the nuance is a little different.

• ограничение по весу = a limit based on weight
• ограничение веса = literally restriction of weight, which can sound less natural in this specific bureaucratic context

In official or practical language, ограничение по весу is the more idiomatic phrase for weight limit.

This means for personal use.

The preposition для (for) requires the genitive case, so:

• личное → личного
• пользование → пользования

That is why you get:

• для личного пользования

This is a very common official expression, especially in customs, travel, and legal contexts.

Because личного is an adjective agreeing with пользования.

The noun пользование is in the genitive singular after для, so the adjective has to match it:

• nominative: личное пользование
• genitive: личного пользования

So личного is simply the genitive singular form of личный.

It is the prepositional case.

The preposition в can take different cases, but when it means in / inside / within a place or document, it usually takes the prepositional:

• декларация → в декларации
• таможенная декларация → в таможенной декларации

So:

• в таможенной декларации = in the customs declaration

Both words change because the adjective must agree with the noun:

• таможенная → таможенной
• декларация → декларации

Russian normally does not use a present-tense equivalent of is / are in sentences like this.

So:

• Ограничение ... указано ... literally feels like
• The limit ... indicated ...

but in correct English we say:

• The limit ... is indicated ...

If you wanted past or future, Russian would add a form of быть:

• было указано = was indicated
• будет указано = will be indicated

But in the present tense, the linking verb is usually omitted.

The word order is quite normal for formal written Russian.

• Ограничение по весу для личного пользования = topic, what the sentence is about
• указано = the main statement
• в таможенной декларации = where it is stated

Russian word order is flexible, so other orders are possible, for example:

• В таможенной декларации указано ограничение по весу для личного пользования.

This version puts more emphasis on where the information is found.
The original sentence sounds neutral and official.

They are related, but not always interchangeable.

In everyday English both can often be translated as use, but in official phrases:

• для личного пользования is a fixed, standard expression meaning for personal use
• для личного использования is possible in some contexts, but it is less standard here

In customs and legal language, для личного пользования is the phrase you are most likely to see.

It sounds formal, official, and bureaucratic.

This is the kind of sentence you might read:

• in a customs form
• on a government website
• in travel regulations
• in an official notice

In casual speech, a person might say something simpler, like:

• Там в декларации написан лимит по весу для личных вещей.
• В декларации указано, сколько можно провозить по весу.

So the original is correct and natural, but it belongs to a formal register.

A natural translation would be:

• The weight limit for personal use is stated in the customs declaration.

Other good translations are:

• The weight restriction for personal use is indicated in the customs declaration.
• The weight limit for personal use is specified in the customs declaration.

In this context, stated or specified often sounds the most natural in English.