Learn Italian: Dove metto questo faldone pesante? - Where do I put this heavy binder?

You would attach it directly to the verb to make rimetto. The sentence becomes Dove rimetto questo faldone pesante? (Where do I put this heavy binder back?). The prefix ri- acts just like 're-' in English, indicating repetition or returning something to its previous state.

Does the word faldone also use a morphological suffix?

Yes, it uses the augmentative suffix -one, which indicates that something is large. The root is falda (a fold or flap). Adding -one creates faldone, literally a 'big fold', which is the standard term for a large document folder or thick binder.

English would usually say 'Where should I put...'. Why does this sentence just use the present tense metto?

In Italian, the simple present indicative is naturally used to ask for immediate instructions or to offer help right now. Saying Dove metto...? is the most common way to say 'Where should I put...?' or 'Where do you want me to put...?'. You don't need to overcomplicate it with a modal verb like dovere (must/should).

Pesante looks like a verb form. Is it?

Yes, it originates from the present participle of pesare (to weigh), formed with the -ante suffix. While it functions purely as a standard adjective here (heavy), its literal morphological origin is 'weighing'. Because it describes a literal, objective physical quality, it is placed directly after the noun.