You are right that Fascism is dependent on the support of the burgeoise and the more “acceptable” right (“centrists”). But It’s a weird way to phrase it that fascism thrives “when the left is weak”. Crisis in the capitalist system opens the door for radical movements from the left as well as the right. A rise in fascism is most often a reaction on a economic crisis brought on by the inherent contradictions capitalism creates. This crisis opens the door for socialist movements which in turn makes the burgeoise support far right movements to combat the left. sometimes it results in fascist takeover (Nazi germany, Pinochet’s Chile) and sometimes in stronger communist ando socialist positions (Russian revolution, Yugoslavia, the social democratic era of northen Europe). But I think you would be hard pressed to describe the German communist movement in the inter war period Up to the Nazi takeover, or the Chilean left as “weak” even if they lost this particular battle (with catastrophic results for the people and nations that had to live through it)