The problem requires a cost-effective, scalable, and secure strategy to anonymize 3 TB of PII in BigQuery and Cloud SQL.

Cloud Sensitive Data Protection (Cloud DLP): Cloud DLP is Google Cloud's fully managed service designed for discovering, classifying, and de-identifying sensitive data, including PII, across various Google Cloud services and on-premises environments. It is specifically built for scale and security.

Extract Reference: "Sensitive Data Protection helps you discover, classify, and de-identify sensitive data." and "Sensitive Data Protection includes advanced de-identification techniques, such as tokenization, masking, and format-preserving encryption, to help you protect your sensitive data while preserving its utility for analysis." (Google Cloud Documentation: "Sensitive Data Protection overview" - https://cloud.google.com/sensitive-data-protection/docs/overview)

Data Profiling: Cloud DLP's data profiling feature automatically scans your data (e.g., BigQuery tables, Cloud SQL databases) to identify where sensitive data resides and to understand its characteristics. This is crucial for developing an effective de-identification strategy.

Extract Reference: "Data profiles provide metrics and insights about your sensitive and high-risk data, helping you make informed decisions about data protection, access, and storage." and "When you configure Sensitive Data Protection to profile data in BigQuery, Cloud Storage, and Datastore, it automatically scans your data for sensitive information." (Google Cloud Documentation: "About data profiles" - https://cloud.google.com/sensitive-data-protection/docs/concepts-data-profiles)

De-identification Templates and Custom Configurations: After profiling identifies the PII, Cloud DLP offers various de-identification methods, which can be applied using pre-built templates or custom configurations. This allows for flexible and targeted anonymization. For BigQuery specifically, DLP can integrate with remote functions for de-identification at query time, minimizing data movement.

Extract Reference: "De-identification techniques, like encryption, obfuscate raw sensitive identifiers in your data. These techniques let you preserve the utility of your data for joining or analytics, while reducing the risk of handling the data." and "You can use this tutorial to replace that pipeline with a SQL query for only re-identification or both de-identification and re-identification." (Google Cloud Documentation: "De-identify BigQuery data at query time | Sensitive Data Protection Documentation" - https://cloud.google.com/sensitive-data-protection/docs/deidentify-bq-tutorial)

Let's evaluate the other options:

B. Copy small subset... create a custom anonymization script... apply the script to the entire 3 TB dataset: Relying on a "custom anonymization script" for 3 TB of data is generally not scalable, cost-effective, or secure compared to a managed service like Cloud DLP. Custom scripts require significant development, testing, maintenance, and robust error handling for large datasets, and might introduce security vulnerabilities.

C. Export all 3TB of data... to Cloud Storage... anonymize... Re-import: While feasible, exporting and re-importing 3 TB of data is a very time-consuming and potentially costly process due to data transfer and storage operations. Cloud DLP can often process data in-place or integrate more efficiently, especially with BigQuery. This option might not be the most cost-effective or efficient.

D. Inspect a representative sample... develop a custom script: Similar to option B, this relies on a custom script, which is less ideal for scalability, cost-effectiveness, and security than a managed service like Cloud DLP for 3 TB of sensitive data. Sample inspection is a good initial step, but the subsequent custom script for anonymization is the weak point.

Therefore, using Cloud DLP's data profiling to inform a de-identification strategy with its managed templates and configurations is the most appropriate, scalable, secure, and cost-effective approach for anonymizing PII in BigQuery and Cloud SQL.