diff --git a/.gitignore b/.gitignore
index d88dd7b7..6e53458d 100644
--- a/.gitignore
+++ b/.gitignore
@@ -68,3 +68,4 @@ tests/integration/sample_extension/src/sample_extension.c
 
 # Downloaded by test script
 tests/integration/patchelf-0.17.2.1-py2.py3-none-manylinux_2_5_x86_64.manylinux1_x86_64.musllinux_1_1_x86_64.whl
+tests/integration/cryptography-46.0.3-cp38-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.whl
diff --git a/noxfile.py b/noxfile.py
index 2bc2c241..ffc2483c 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -59,6 +59,27 @@ def _docker_images(session: nox.Session) -> list[str]:
     return images_file.read_text().splitlines()
 
 
+def _download_wheels_for_tests(session: nox.Session) -> None:
+    wheels = [
+        # for tests/integration/test_bundled_wheels.py::test_analyze_wheel_abi_static_exe
+        ("patchelf==0.17.2.1", "py38", "manylinux1_x86_64"),
+        # for tests/integration/test_bundled_wheels.py::test_weak_symbols_not_blacklisted
+        ("cryptography==46.0.3", "cp38", "manylinux_2_17_x86_64"),
+    ]
+    for package, python_tag, platform in wheels:
+        session.run(
+            "pip",
+            "download",
+            "--only-binary=:all:",
+            "--no-deps",
+            "--dest=./tests/integration/",
+            f"--platform={platform}",
+            f"--implementation={python_tag[:2]}",
+            f"--python-version={python_tag[2:]}",
+            package,
+        )
+
+
 @nox.session(python=PYTHON_ALL_VERSIONS, default=False)
 def tests(session: nox.Session) -> None:
     """Run tests."""
@@ -68,19 +89,8 @@ def tests(session: nox.Session) -> None:
     deps = nox.project.dependency_groups(pyproject, dep_group)
     session.install("-U", "pip")
     session.install("-e", ".", *deps)
-    # for tests/integration/test_bundled_wheels.py::test_analyze_wheel_abi_static_exe
-    session.run(
-        "pip",
-        "download",
-        "--only-binary",
-        ":all:",
-        "--no-deps",
-        "--platform",
-        "manylinux1_x86_64",
-        "-d",
-        "./tests/integration/",
-        "patchelf==0.17.2.1",
-    )
+    _download_wheels_for_tests(session)
+
     if RUNNING_CI:
         posargs.extend(["--cov", "auditwheel", "--cov-config", "pyproject.toml"])
         # pull manylinux images that will be used.
@@ -135,6 +145,7 @@ def develop(session: nox.Session) -> None:
     pyproject = nox.project.load_toml("pyproject.toml")
     deps = nox.project.dependency_groups(pyproject, "dev")
     session.install("-e", ".", *deps)
+    _download_wheels_for_tests(session)
 
 
 if __name__ == "__main__":
diff --git a/src/auditwheel/elfutils.py b/src/auditwheel/elfutils.py
index 142d55a7..f375a20c 100644
--- a/src/auditwheel/elfutils.py
+++ b/src/auditwheel/elfutils.py
@@ -131,8 +131,9 @@ def get_undefined_symbols(path: Path) -> set[str]:
         section = elf.get_section_by_name(".dynsym")
         if section is not None:
             # look for all undef symbols
+            # if the symbol is weak don't consider it as undefined, it's "optional"
             for sym in section.iter_symbols():
-                if sym["st_shndx"] == "SHN_UNDEF":
+                if sym["st_shndx"] == "SHN_UNDEF" and sym["st_info"]["bind"] != "STB_WEAK":
                     undef_symbols.add(sym.name)
     return undef_symbols
 
diff --git a/tests/integration/test_bundled_wheels.py b/tests/integration/test_bundled_wheels.py
index f402a5e9..db440ffa 100644
--- a/tests/integration/test_bundled_wheels.py
+++ b/tests/integration/test_bundled_wheels.py
@@ -258,3 +258,20 @@ def test_main_lddtree(
         "libraries": {},
     }
     assert expected_json == actual_json
+
+
+def test_weak_symbols_not_blacklisted() -> None:
+    # https://github.com/pypa/auditwheel/issues/663
+    # the cryptography wheel overall policy was misclassified as manylinux_2_24_x86_64
+    # in auditwheel 6.5.1 because it uses the undefined weak symbol '__cxa_thread_atexit_impl'
+    result = analyze_wheel_abi(
+        None,
+        None,
+        HERE / "cryptography-46.0.3-cp38-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.whl",
+        frozenset(),
+        disable_isa_ext_check=False,
+        allow_graft=False,
+    )
+    assert result.policies.libc == Libc.GLIBC
+    assert result.policies.architecture == Architecture.x86_64
+    assert result.overall_policy.name == "manylinux_2_17_x86_64"