line up, be in a row, rank with, rival, equal
竝 centers on things being side by side in a line or on equal standing: lining up, being in a row, ranking with others, or being a rival or equal.
竝 is the older form of 並, showing two 立 (standing) figures side by side to express lining up or being equal. The modern 並 is a simplified variant.
Two 立 (standing) figures placed side by side, like people lining up in a row or standing as equals.
For ヘイ, picture two people lining up to say 'hey' to each other: hey -> ヘイ, as they stand side by side.