diff --git a/scrapy_zyte_api/providers.py b/scrapy_zyte_api/providers.py
index 19371666..fb04554f 100644
--- a/scrapy_zyte_api/providers.py
+++ b/scrapy_zyte_api/providers.py
@@ -1,5 +1,4 @@
 from typing import Any, Callable, Dict, List, Sequence, Set
-from weakref import WeakKeyDictionary
 
 from andi.typeutils import is_typing_annotated, strip_annotated
 from scrapy import Request
@@ -51,30 +50,35 @@ class ZyteApiProvider(PageObjectInputProvider):
         JobPosting,
     }
 
-    def __init__(self, injector):
-        super().__init__(injector)
-        self._cached_instances: WeakKeyDictionary[Request, Dict] = WeakKeyDictionary()
-
     def is_provided(self, type_: Callable) -> bool:
         return super().is_provided(strip_annotated(type_))
 
     def update_cache(self, request: Request, mapping: Dict[Any, Any]) -> None:
-        if request not in self._cached_instances:
-            self._cached_instances[request] = {}
-        self._cached_instances[request].update(mapping)
+        if request not in self.injector.weak_cache:
+            self.injector.weak_cache[request] = {}
+        self.injector.weak_cache[request].update(mapping)
 
     async def __call__(  # noqa: C901
         self, to_provide: Set[Callable], request: Request, crawler: Crawler
     ) -> Sequence[Any]:
         """Makes a Zyte API request to provide BrowserResponse and/or item dependencies."""
-        # TODO what if ``response`` is already from Zyte API and contains something we need
         results: List[Any] = []
 
         for cls in list(to_provide):
-            item = self._cached_instances.get(request, {}).get(cls)
+            item = self.injector.weak_cache.get(request, {}).get(cls)
             if item:
                 results.append(item)
                 to_provide.remove(cls)
+            elif cls == AnyResponse:
+                http_response = self.injector.weak_cache.get(request, {}).get(
+                    HttpResponse
+                )
+                if http_response:
+                    any_response = AnyResponse(response=http_response)
+                    results.append(any_response)
+                    self.update_cache(request, {AnyResponse: any_response})
+                    to_provide.remove(cls)
+
         if not to_provide:
             return results
 
@@ -170,7 +174,7 @@ async def __call__(  # noqa: C901
             self.update_cache(request, {BrowserResponse: browser_response})
 
         if AnyResponse in to_provide:
-            any_response = None
+            any_response = None  # type: ignore[assignment]
 
             if "browserHtml" in api_response.raw_api_response:
                 any_response = AnyResponse(
diff --git a/setup.py b/setup.py
index a5c15648..f79c380a 100644
--- a/setup.py
+++ b/setup.py
@@ -31,7 +31,8 @@ def get_version():
         # Sync with [testenv:pinned-provider] @ tox.ini
         "provider": [
             "andi>=0.6.0",
-            "scrapy-poet>=0.19.0",
+            # "scrapy-poet>=0.19.0",
+            "scrapy-poet @ git+https://git@github.com/scrapinghub/scrapy-poet@weak-cache#egg=scrapy-poet",
             # "web-poet>=0.15.1",
             "web-poet @ git+https://git@github.com/scrapinghub/web-poet@response#egg=web-poet",
             "zyte-common-items>=0.8.0",
diff --git a/tests/test_providers.py b/tests/test_providers.py
index 9eb4e1bc..b0fd0d6a 100644
--- a/tests/test_providers.py
+++ b/tests/test_providers.py
@@ -551,6 +551,10 @@ def parse_(self, response: DummyResponse, page: SomePage):
     assert type(item["page"].product) == Product
 
 
+# The issue here is that HttpResponseProvider runs earlier than ScrapyZyteAPI.
+# HttpResponseProvider doesn't know that it should not run since ScrapyZyteAPI
+# could provide HttpResponse in anycase.
+@pytest.mark.xfail(reason="Not supported yet", raises=AssertionError, strict=True)
 @ensureDeferred
 async def test_provider_any_response_product_extract_from_http_response_2(mockserver):
     @attrs.define
@@ -688,10 +692,15 @@ def parse_(self, response: DummyResponse, page: SomePage):
     params = crawler.engine.downloader.handlers._handlers["http"].params
 
     assert len(params) == 1
-    assert params[0].keys() == {"url", "HttpResponseBody"}
+    assert params[0].keys() == {
+        "url",
+        "httpResponseBody",
+        "customHttpRequestHeaders",
+        "httpResponseHeaders",
+    }
 
     assert type(item["page"].response) == AnyResponse
-    assert type(item["page"].response.response) == BrowserResponse
+    assert type(item["page"].response.response) == HttpResponse
     assert type(item["page"].http_response) == HttpResponse
 
 
@@ -715,10 +724,15 @@ def parse_(self, response: DummyResponse, page: SomePage):
     params = crawler.engine.downloader.handlers._handlers["http"].params
 
     assert len(params) == 2
-    assert params[0].keys() == {"url", "HttpResponseBody"}
-    assert params[1].keys() == {"url", "BrowserHtml"}
+    assert params[0].keys() == {
+        "url",
+        "httpResponseBody",
+        "customHttpRequestHeaders",
+        "httpResponseHeaders",
+    }
+    assert params[1].keys() == {"url", "browserHtml"}
 
     assert type(item["page"].response) == AnyResponse
-    assert type(item["page"].response.response) == BrowserResponse
+    assert type(item["page"].response.response) == HttpResponse
     assert type(item["page"].browser_response) == BrowserResponse
     assert type(item["page"].http_response) == HttpResponse
diff --git a/tox.ini b/tox.ini
index 3a4d38fe..d0da523d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -89,7 +89,8 @@ deps =
     # scrapy-poet >= 0.4.0 depends on scrapy >= 2.6.0
     {[testenv:pinned-scrapy-2x6]deps}
     andi==0.6.0
-    scrapy-poet==0.19.0
+    #scrapy-poet==0.19.0
+    scrapy-poet @ git+https://git@github.com/scrapinghub/scrapy-poet@weak-cache#egg=scrapy-poet
     #web-poet==0.15.1
     web-poet @ git+https://git@github.com/scrapinghub/web-poet@response#egg=web-poet
     zyte-common-items==0.8.0