diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 1f0b1621013..8599563b60b 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -51,9 +51,15 @@ jobs:
         python -m pip install .
       env:
         AIOHTTP_NO_EXTENSIONS: 1
-    - name: Run linters
+    - name: Run mypy
       run: |
         make mypy
+    - name: Run slotscheck
+      run: |
+        # Some extra requirements are needed to ensure all modules
+        # can be scanned by slotscheck.
+        pip install -r requirements/base.txt -c requirements/constraints.txt
+        slotscheck -v -m aiohttp
     - name: Install libenchant-dev
       run: |
         sudo apt install libenchant-dev
diff --git a/CHANGES/6547.bugfix b/CHANGES/6547.bugfix
new file mode 100644
index 00000000000..8512c4067f6
--- /dev/null
+++ b/CHANGES/6547.bugfix
@@ -0,0 +1,2 @@
+Remove overlapping slots in ``RequestHandler``,
+fix broken slots inheritance in :py:class:`~aiohttp.web.StreamResponse`.
diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt
index d8be9a57a0f..a9f82da88ef 100644
--- a/CONTRIBUTORS.txt
+++ b/CONTRIBUTORS.txt
@@ -46,6 +46,7 @@ Anes Abismail
 Antoine Pietri
 Anton Kasyanov
 Anton Zhdan-Pushkin
+Arie Bovenberg
 Arseny Timoniq
 Artem Yushkovskiy
 Arthur Darcet
diff --git a/aiohttp/helpers.py b/aiohttp/helpers.py
index b7a033795fb..febc49647c5 100644
--- a/aiohttp/helpers.py
+++ b/aiohttp/helpers.py
@@ -831,9 +831,17 @@ def __repr__(self) -> str:
 
 
 class CookieMixin:
+    # The `_cookies` slots is not defined here because non-empty slots cannot
+    # be combined with an Exception base class, as is done in HTTPException.
+    # CookieMixin subclasses with slots should define the `_cookies`
+    # slot themselves.
+    __slots__ = ()
+
     def __init__(self) -> None:
         super().__init__()
-        self._cookies: SimpleCookie[str] = SimpleCookie()
+        # Mypy doesn't like that _cookies isn't in __slots__.
+        # See the comment on this class's __slots__ for why this is OK.
+        self._cookies: SimpleCookie[str] = SimpleCookie()  # type: ignore[misc]
 
     @property
     def cookies(self) -> "SimpleCookie[str]":
diff --git a/aiohttp/web_protocol.py b/aiohttp/web_protocol.py
index 03d0c274719..6d662949d8f 100644
--- a/aiohttp/web_protocol.py
+++ b/aiohttp/web_protocol.py
@@ -170,7 +170,6 @@ class RequestHandler(BaseProtocol):
         "_upgrade",
         "_payload_parser",
         "_request_parser",
-        "_reading_paused",
         "logger",
         "access_log",
         "access_logger",
diff --git a/aiohttp/web_response.py b/aiohttp/web_response.py
index 42c3fac51ae..6ac280ebefa 100644
--- a/aiohttp/web_response.py
+++ b/aiohttp/web_response.py
@@ -92,6 +92,7 @@ class StreamResponse(BaseClass, HeadersMixin, CookieMixin):
         "_headers",
         "_status",
         "_reason",
+        "_cookies",
         "__weakref__",
     )
 
diff --git a/requirements/lint.txt b/requirements/lint.txt
index c4949763d70..0324cc84401 100644
--- a/requirements/lint.txt
+++ b/requirements/lint.txt
@@ -2,3 +2,4 @@
 mypy==0.931; implementation_name=="cpython"
 pre-commit==2.17.0
 pytest==6.2.5
+slotscheck==0.8.0
diff --git a/tests/test_helpers.py b/tests/test_helpers.py
index 9cfebc7b3a6..26afe82ef7e 100644
--- a/tests/test_helpers.py
+++ b/tests/test_helpers.py
@@ -850,8 +850,14 @@ def test_is_expected_content_type_non_json_not_match():
     )
 
 
+# It's necessary to subclass CookieMixin before using it.
+# See the comments on its __slots__.
+class CookieImplementation(helpers.CookieMixin):
+    pass
+
+
 def test_cookies_mixin():
-    sut = helpers.CookieMixin()
+    sut = CookieImplementation()
 
     assert sut.cookies == {}
     assert str(sut.cookies) == ""
@@ -880,7 +886,7 @@ def test_cookies_mixin():
 
 
 def test_cookies_mixin_path():
-    sut = helpers.CookieMixin()
+    sut = CookieImplementation()
 
     assert sut.cookies == {}
 
@@ -914,7 +920,7 @@ def test_cookies_mixin_path():
 
 
 def test_sutonse_cookie__issue_del_cookie():
-    sut = helpers.CookieMixin()
+    sut = CookieImplementation()
 
     assert sut.cookies == {}
     assert str(sut.cookies) == ""
@@ -928,7 +934,7 @@ def test_sutonse_cookie__issue_del_cookie():
 
 
 def test_cookie_set_after_del():
-    sut = helpers.CookieMixin()
+    sut = CookieImplementation()
 
     sut.del_cookie("name")
     sut.set_cookie("name", "val")
@@ -938,7 +944,7 @@ def test_cookie_set_after_del():
 
 
 def test_populate_with_cookies():
-    cookies_mixin = helpers.CookieMixin()
+    cookies_mixin = CookieImplementation()
     cookies_mixin.set_cookie("name", "value")
     headers = CIMultiDict()