I know ほど means ‘degree’ or ‘extent’ and so 僕のほど might translate as ‘to my extent’ but I don’t see how that possible translation fits with the rest of the sentence’s meaning.
彼女が僕に対して持っている気持ちは、僕のほど強くないようだ。
My translation: The feelings she holds against me don’t seem to be that strong.
The way I read this, you shouldn't see it as 僕のほど with の as the 'possessive' like 僕の猫, but rather view の here as acting like a quasi-pronoun. Like "彼女の車は青い。僕のは黒い。"
僕の(気持ち)ほど強くないようだ
ほど often follows a noun directly without a の outside of keigo, and I think this is one of those situations.
So you could read the sentence as:
It seems that the feelings she has for me aren't as strong as mine.
