Learn Spanish (Latin America): A pesar de que el barco es pesado, todavía flota. - Even though the boat is heavy, it still floats.

We use the indicative (es) here because the fact that the boat is heavy is treated as a known, established reality. If we were talking about a hypothetical situation ('Even if the boat were heavy...'), we would use the subjunctive sea.

Why do we need the que in a pesar de que? Can we just say a pesar de?

You need que whenever a conjugated verb follows. Since es is a conjugated verb forming a full clause, we must use a pesar de que. If you were just using a noun phrase without a verb, like 'Despite the heavy boat', you would drop the que and say a pesar del barco pesado.

Why use es pesado instead of está pesado?

We use ser (here, es) because being heavy is seen as a permanent, inherent characteristic of the boat's design. If you used estar (está pesado), it would imply a temporary state, like a suitcase that happens to be heavy today because you packed too much.

I have seen todavía used for 'yet'. How do I know it means 'still' here?