The correct answer to fill in the blank would be "increase" in the first part of the sentence and "eukaryotic cells" in the second part.
So the completed sentence would be:
"Increased levels of oxygen in the atmosphere due to photosynthesis caused rates of weathering to increase, which aided in the formation of eukaryotic cells."
(Note: If "eukaryotic cells" is not an option, please provide a relevant list, and I can assist you in selecting the correct term.)