という理由（りゆう）で is a phrase that is used when giving reasons for (A). (A) may be a range of different things, from what happened, to what one’s opinion is. Due to という quoting the previous statement as being the ‘reason’,
という理由（りゆう）で puts quite a bit of emphasis on the reason itself. Because of this, the expression is quite similar to ‘being that’ in English.
The 格助詞（かくじょし） (case marking particle) で will be used after 理由（りゆう） to show that ‘with’ or ‘by means of’ that reason, (B).
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コストコは安（やす）く沢山（たくさん）買（か）い物（もの）が出来（でき）るという理由（りゆう）で人気（にんき）がある。
At Costco, you can shop for many things at a cheap price. For that reason it is popular.
大変（たいへん）だという理由（りゆう）で彼（かれ）は仕事（しごと）を辞（や）めた。
Being that his job was a hassle, he resigned.
Almost all cases where
という理由（りゆう）で will be used may be replaced by というわけで. However, the reverse is not true.
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安（やす）くて美味（おい）しいという理由（りゆう）で、この店（みせ）の前（まえ）にはいつも行列（ぎょうれつ）ができています。
Being that this place is cheap and delicious, they always have a long line in front of the store.
一人（ひとり）で行（い）きたくないという訳（わけ）では無（な）いです。一人（ひとり）で行（い）くのは危（あぶ）ないと言（い）いたいのです。
It is not so that I don't want to go alone. I am saying that it is dangerous to go alone.
という理由（りゆう）で、この企画（きかく）はキャンセルすることにします。 (Unnatural)
For that reason, we are going to cancel this plan.
というわけで、この企画（きかく）はキャンセルすることにします。 (Natural)
Well with that, we will decide on canceling this plan.
The reason that わけ may be used for 理由（りゆう）, but 理由（りゆう） cannot always be used for わけ (especially at the beginning of sentences) is because 理由（わけ） is another way of reading the kanji for 理由（りゆう）. However, the more common kanji for 訳（わけ） will never be read as りゆう.