Learn Italian: Non posso sopportare questo odoraccio. - I cannot tolerate this bad smell.

The base word is odore (smell). To add the pejorative suffix, we drop the final vowel 'e' and add -accio. Since odore is a masculine noun, it takes the masculine suffix, giving us odoraccio (a nasty smell).

Does the -accio ending just mean 'bad', or does it add a specific emotion here?

It adds a strong sense of personal disgust or annoyance. While you could simply say cattivo odore (bad smell), using the suffix -accio makes it much more expressive. It shows the speaker finds the stench truly foul and offensive.

Why is there no preposition between posso and sopportare?

Because potere (here conjugated as posso) is a modal verb, acting just like the English helper verbs 'can' or 'must'. In Italian, modal verbs always link directly to the infinitive form of the next verb (sopportare) without needing any linking prepositions like a or di.

Can sopportare be used for carrying physical weight, or only for tolerating things like this smell?

It works for both! Sopportare translates to 'to bear', 'to endure', or 'to tolerate'. You can use it when talking about a pillar bearing heavy weight, enduring physical pain, or putting up with an awful smell like the one in this sentence.