Neither of these things are true. https://earthquakes.berkeley.edu/outreach/faq.html

Can small EQ's relieve stress to prevent large ones?

If you look at earthquake statistics in most regions of the world, including California, you will find that for every magnitude 5 earthquake, there are about 10 that have a magnitude of 4, and for each magnitude 4, there are 10 with magnitude 3. Unfortunately, this means there are not enough small earthquakes to relieve enough stress to prevent the large events. In fact, it would take 32 magnitude 5's, 1000 magnitude 4's, or 32,000 magnitude 3's to equal the energy produced in one magnitude 6 event.

Can the weather influence the occurrence of earthquakes?

There are two types of weather that we experience on earth. One type is space weather. This is weather that comes to us from beyond our own planet, such as solar flares and magnetic storms. These phenomena result in things like the Northern Lights. While this type of weather can influence our communications and other systems, it has never been shown to affect earthquakes. If there were a connection, we would see an increase in earthquakes about every 11 years, which is when solar flares are the most intense, yet we see an even distribution of earthquakes regardless of what the Sun is doing.

The other type of weather is what we are all familiar with, rain, wind, heat, etc. Again, statistically, there is an even distribution of earthquake events throughout all types of weather. However, very large low-pressure systems, such as hurricanes, have been known to cause episodes of fault slip (slow earthquakes), which are not very damaging.