The quota for a web app seems to differ from that of a hybrid app (as in something running within a view). Regardless, by implementing the following in your android.app.Activity
subclass you will double the quota until it finally stops at approximately 48MB.
@Override
public void onExceededDatabaseQuota(String url, String databaseIdentifier, long currentQuota, long estimatedSize, long totalUsedQuota, WebStorage.QuotaUpdater quotaUpdater) {
quotaUpdater.updateQuota(estimatedSize * 2);
}
The user will not be asked to interact when this happens.