Learning grammar also helps a lot with parsing sentences. くださる (like くれる) can be attached to a verb in て-form to indicate that the verb was done for the speaker. This makes 見てくださり basically “saw (for my benefit)”, where the part I put in parentheses is often left out of English translations. Further, after て-form of くださる (again like くれる) you can put things like 嬉しい, ありがとう, etc. to indicate your feelings or thanks for that action being done for you. In more formal situations, the て-form can be replaced with the verb stem, in this case くださり. Hence, the whole thing loosely translates to “I’m happy that you saw (for my benefit)”.
In short, it becomes a lot easier to parse sentences when you know the grammar.