'Biggest" translates very poorly. I tried both 'highest' and 'deepest', and both were rejected, although those are by far the most common ways an English-speaker would communicate this feeling.
I"m an english speaker, American, and I'd say 'great respect' or 'greatest respect'.
I agree. I like "great respect" or "highest esteem," "biggest esteem" doesn't sound right.
But "plus grand" is a superlative; so "greatest", "biggest" i.e. the most, isn't it. So "great", on its own, wouldn't be quite (most) great enough. Utmost / greatest works for me. Would, "Tu as notre grand estime, mais ton ami a notre plus grand estime" make sense?
I don't understand why this wouldn't be "Nous avons vous plus grande estime"