When we say a blessing, we are not blessing Hashem. We are not saying Blessed be Hashem…. The translation is, "Blessed is Hashem". This means that Hashem is the source of all blessings. By recognizing this we are praising Him.
King Dovid said enter His gates with thanksgiving and His courtyard with praise. When we do a mitzvah, if we are thankful for the opportunity…, for the spiritual tool Hashem has given us, then, when we say the blessing we are moving through His outer gate and on into His courtyard. Indeed, it is a privilege to be a Jew.