Is the word pesar the same in Brazilian and European Portuguese?

Yes

The word "pesar" is identical in both Brazilian and Continental Portuguese in terms of meaning, spelling, and grammatical function. The differences between the two variants are strictly phonological (pronunciation). In Brazilian Portuguese, vowels tend to be more open and clearly articulated, whereas in Continental Portuguese, unstressed vowels are often reduced or even swallowed (a phenomenon known as vowel reduction). Additionally, the "s" sound in many Brazilian dialects is more consistent, while in Portugal, the "s" before a consonant is typically pronounced as a "sh" sound (palatalization).

Brazilian Portuguese Examples:

1. Quanto pesa essa mala? (How much does that suitcase weigh?)

2. A notícia da demissão pesou muito para ele. (The news of the layoff weighed heavily on him.)

3. A culpa pesa na minha consciência. (Guilt weighs on my conscience.)

4. O colar pesa bastante no pescoço. (The necklace weighs quite a bit on the neck.)

5. Essa situação pesa no meu dia a dia. (This situation weighs on my daily life.)

Portuguese (Portugal) Examples:

1. Quanto pesa esta mala? (How much does this suitcase weigh?)

2. A notícia do despedimento pesou-lhe muito. (The news of the dismissal weighed heavily on him.)

3. A culpa pesa na minha consciência. (Guilt weighs on my conscience.)

4. O colar pesa bastante no pescoço. (The necklace weighs quite a bit on the neck.)

5. Essa situação pesa no meu quotidiano. (This situation weighs on my daily life.)