First, ensure you have Python installed on your computer, as it will be used to interact with both Gutendex and Weaviate. Install necessary Python libraries using pip, such as `requests` for making HTTP requests, and `weaviate-client` for interacting with Weaviate. You can do this by running `pip install requests weaviate-client` in your terminal.

Utilize the Gutendex API to retrieve data. You can access the API by sending an HTTP GET request to the Gutendex API endpoint. For example, use:
```python
import requests

response = requests.get('http://gutendex.com/books')
data = response.json()
```
This will fetch the list of books in JSON format. You can adjust the endpoint parameters to filter or paginate the data as needed.

Parse the JSON data retrieved from Gutendex and clean it according to your requirements. This involves selecting relevant fields, handling any missing or malformed data, and possibly transforming the data format to match the schema you plan to use in Weaviate.
```python
books = data.get('results', [])
processed_books = [{
'title': book.get('title'),
'author': ', '.join(author['name'] for author in book.get('authors', [])),
'language': book.get('languages', [])[0] if book.get('languages') else 'unknown'
} for book in books]
```

Ensure that Weaviate is up and running. You can run Weaviate locally using Docker or access a cloud-hosted instance. Configure Weaviate to accept connections, typically by setting up the schema for your data. Define classes and properties that match the data structure you prepared in the previous step.

Before data can be added to Weaviate, you need to define the appropriate schema. This involves specifying the classes and their properties that will hold your data. Use the Weaviate client to push your schema:
```python
import weaviate

client = weaviate.Client("http://localhost:8080")
schema = {
"classes": [
{
"class": "Book",
"properties": [
{"name": "title", "dataType": ["text"]},
{"name": "author", "dataType": ["text"]},
{"name": "language", "dataType": ["text"]}
]
}
]
}
client.schema.create(schema)
```

With the schema defined, you can now insert your processed data into Weaviate. Use the Weaviate client to batch insert records for efficiency:
```python
with client.batch as batch:
batch.batch_size = 100
for book in processed_books:
batch.add_data_object(book, "Book")
```
This code batches the data objects to minimize the number of network requests, improving efficiency.

After inserting data, verify that all entries have been correctly added to Weaviate. This can be done by querying the data back from Weaviate and checking for consistency with your original dataset:
```python
result = client.query.get("Book", ["title", "author", "language"]).do()
print(result)
```
Ensure that the number of records matches and that key fields are populated correctly. This step is crucial for validating the success of your data transfer process.

Following these steps will allow you to transfer data from Gutendex to Weaviate effectively without the need for third-party connectors or integrations.