```python
def line_tag(body: str) -> str:
    """Compute the tag of a body as the sum of its character codes modulo 256,
    rendered as exactly two lowercase hexadecimal digits, zero-padded."""
    if not isinstance(body, str):
        raise ValueError("Body must be a string")
    return format(sum(ord(c) for c in body) % 256, '02x')

def check_line(line: str) -> str:
    """Verify a tagged line and return its body. The third-from-last character
    must be a tilde and the last two characters must equal the tag computed by
    line_tag for everything before that tilde."""
    if not isinstance(line, str):
        raise ValueError("Line must be a string")
    if len(line) < 3:
        raise ValueError("Line must be at least three characters long")
    if line[-3] != '~':
        raise ValueError("Third-from-last character must be a tilde")
    tag = line[-2:]
    body = line[:-3]
    if tag != line_tag(body):
        raise ValueError("Tag does not match the body")
    return body
```