Мой брат любит теннис и часто играет в теннис по выходным.

Because брат is a masculine singular noun in the nominative case, and the possessive pronoun has to agree with it.

• мой = masculine singular
• моя = feminine singular
• моё = neuter singular
• мои = plural

So:

• мой брат = my brother
• моя сестра = my sister

Russian does not have articles like English a/an and the. Whether something is definite or indefinite is usually understood from context.

So брат can mean brother, a brother, or the brother depending on context. In this sentence, мой брат naturally means my brother.

They express two different ideas:

• любит теннис = he likes/loves tennis
• играет в теннис = he plays tennis

So the sentence says both:

1. He likes the sport.
2. He often plays it.

In Russian, любить is about liking something, while играть в describes taking part in a game or sport.

Yes, absolutely.

• любит теннис = he likes tennis in general
• любит играть в теннис = he likes playing tennis

The original sentence is a little broader: it says he likes tennis as a sport, and then adds that he often plays it on weekends. If you say любит играть в теннис, the focus is more specifically on the activity of playing.

Because Russian normally uses the pattern играть в + accusative for games and sports.

Examples:

• играть в теннис
• играть в футбол
• играть в шахматы

This is just the standard construction you learn with играть when talking about playing a sport or game.

Compare that with musical instruments, where Russian usually uses a different pattern:

• играть на пианино
• играть на гитаре

So:

• играть в = play a game/sport
• играть на = play an instrument

It actually is in the accusative case in both places, but for this kind of noun, the accusative looks exactly like the nominative.

Why accusative?

• after любит: теннис is the direct object
• after играет в: в takes the accusative here

But теннис is:

• masculine
• singular
• inanimate

For many masculine inanimate nouns in Russian, nominative = accusative in the singular.

So:

• nominative: теннис
• accusative: теннис

That is why there is no visible change.

Yes, Russian could avoid repetition, but repeating the noun is very normal and clear.

The original:

• Мой брат любит теннис и часто играет в теннис по выходным.

Possible alternative:

• Мой брат любит теннис и часто играет в него по выходным.

Here в него means it. But Russian often repeats the noun instead of replacing it with a pronoun, especially when that makes the sentence clearer or more natural.

So the repetition is not wrong or strange.

That is a very natural position for an adverb like часто.

• часто играет = often plays

Russian word order is more flexible than English, but this placement is neutral and common. You could also hear:

• Мой брат часто играет в теннис по выходным.

That version is also very natural. The exact position can slightly change emphasis, but both are fine.

По выходным means on weekends or at weekends.

The word выходным is in the dative plural. This happens because Russian often uses:

• по + dative plural

for repeated time expressions.

So:

• по выходным = on weekends / every weekend
• literally something like on days off

The base word is выходной, which can mean day off or weekend day depending on context.

You may hear на выходных very often in everyday Russian, but по выходным is the better choice here.

Why?

• по выходным clearly means habitually / on weekends in general
• на выходных is very common colloquial Russian, but it often refers to a particular weekend depending on context

So in a sentence about a regular habit, по выходным is especially natural.

Because Russian uses the present tense to talk about regular or habitual actions, just like English does in sentences such as He often plays tennis.

Here the words:

• часто = often
• по выходным = on weekends

show that this is a repeated habit, not something happening only right now.

Also, играет is from the imperfective verb играть, which is exactly what Russian normally uses for repeated, habitual actions.