It is a "simple" sentence, but I can't find any information how I should parse and interpret this part.
これでも用心深いほうなんでね。
Do you already know how to make a comparison using ほう and より in Japanese? If not, please learn it first.
The sentence in question is an extension of this. While there is no explicit comparison target marked with ~より, this ほう still means "comparatively" or "relatively".
これでも用心深いほうなんでね。
Despite my appearance, (if one has to categorize me either as a cautious or as a careless person,) I'm comparatively a cautious person, you know.
I'm a more cautious person than I may look, you know.
これでも (literally "even with this") is a set phrase, "although you may think otherwise" or "although I may not look like it".
Similar examples:
- このケーキは甘いほうだ。 This cake is relatively sweet.
- 私はよく寝るほうです。 I'm relatively a good sleeper.
- あまりテレビは見ないほうです。 I'm not a kind of person who watches TV often.
Related:
方(ほう) is used to make comparisons.
用心深いほう means "the more cautious one".
Examples from プログレッシブ和英中辞典:
4 〔比べられる物の一方〕a side; a part
その小さい方をください
Give me the smaller one.私の方の手落ちでした
The fault was mine.彼の方に不服はなかった
There was no dissatisfaction on his part.私たちは皆彼の方についた
All of us sided with him.生活は今の方が前より楽だ
I am better off than I used to be.
and from デジタル大辞泉:
3 二つ以上あるもののうちの一つをとりあげてさす語。
「黒い方が好きだ」
「もっと味を濃くした方がいい」
「こちらの方が悪かった」
用心深いほう means "the more cautious one".
<-- Nope! It's not #4 but #3 on プログレッシブ和英 「3 〔部類〕 彼は勉強家の方だ He is rather studious./He's on the studious side.」 and not #3 but #4 on デジタル大辞泉 「4 どちらかといえばこちらだという部類。「性質は臆病な方だ」」