2009 Honda Civic - Is climate affecting it starting?

It was slow to turn over one time a day or 2 ago.

It took 2 cranks to turn over this morning. It's a new battery.

Bought the car the beginning of August last year and around the same week (last week of August), my battery died.

A month and a half ago, it was pouring raining and it took 6 cranks over a period of 10 minutes to turn over.

What's going on here? Car hates muggy, rainy weather?

Cranking and turning over are the same thing. You likely mean the motor turns over but doesn't "fire" or "start". When's the last time you had the valves adjusted? All Honda manufactured motors have a common problem with valves getting tight and need adjusting every 60,000 miles. Have you put a set of NGK or Denso Iridium spark plugs in the motor? Have you replaced the air filter or taken the air filter out to check for a mouse nest restricting the air flow? Check the timing belt marks to make sure the timing belt hasn't jumped time.

Hard starting and rough running when it's wet and humid usually point to plug wires that need to be replaced. Have a look under the hood at night in a dark place while the engine is running and look for arcing.