Learn Hardcore Malay: Basikal ini berat.

Malay uses a zero copula for present-tense descriptive or equational sentences. You directly combine the noun phrase and adjective.
Literally Basikal ini berat = bicycle this heavy → this bicycle is heavy

Why does the adjective berat come after the noun, unlike English where adjectives come before?

The default Malay order is Noun + (Demonstrative) + Adjective. Adjectives always follow the nouns they describe.
Hence: Basikal ini berat = this bicycle heavy

How do you say This bicycle is not heavy in Malay?

Place tidak before the adjective:
Basikal ini tidak berat
In informal speech, you can also say:
Basikal ini tak berat

How would you ask Is this bicycle heavy? formally and informally?

Formal: start with adakah:
Adakah basikal ini berat?
Informal: add ke at the end:
Basikal ini berat ke?

How do you express very heavy in Malay?

Insert sangat (very) before the adjective:
Basikal ini sangat berat = this bicycle is very heavy

Do I need to change basikal to make it plural? How do you say These bicycles are heavy?

Malay nouns do not change form for plural; context is enough.
Basikal ini berat can mean this bicycle is heavy or these bicycles are heavy if context shows plurality.
To be explicit, you can:
• Reduplicate: Basikal-basikal ini berat
• Add semua (all): Semua basikal ini berat

How do you say This bicycle is heavier than that one?

Use lebih … daripada for comparisons:
Basikal ini lebih berat daripada basikal itu
Casual form might use dari and drop itu short form:
Basikal ini lebih berat dari basikal tu