Well, the confusion is somehow justified as well because both the words refer to the same natural phenomena, but the different lies in their measurement time.
To put it in simple words, Climate is Weather over a long period of time, like 6 months or a year or even many years, whereas Weather is the instant phenomenon at a given hour or a day. Weather often changes frequently at many places during the day, sometimes changing every 15 minutes as well. However, on a longer average, climate doesn't change that frequently. If it changes that frequently, then it's doomsday for us.
Hence Global Warming is also referred to as Climate Change and not Weather change.
Next time when you greet someone, say "How's the Weather today?"
Cheers.
अभिषेक परमार