“This rise in obesity is due to poor diet and lack of exercise.”

You're writing a blog post about how you think America should solve the problem of having too many overweight people. You just wrote that obesity has increased over the last 20 years. Now you want to explain why you think the number of fat people has increased You write:

This rise in obesity is due to poor diet and lack of exercise.

this (thing)

In academic writing or when giving speeches, you can use "this" to continue talking about a topic from one sentence to the next:

By the end of the century, the number of hungry people in the world began to increase, rising to 798 million in 2001. This increase in hunger is not too surprising, given the lack of growth in the world grain harvest during this period.

a rise in (something)

When the number of something increases, you can talk about the situation with the phrase "a rise in ___". For example:

There's been a rise in the number of companies that are cutting employees.

You use "a rise in ___" in formal English.

(something) is due to (something)

In formal writing, you explain the reason for something by saying that it "is due to ___":

School has been cancelled due to inclement weather.

You have to follow "due to ___" with a noun. So if you want to say that the reason for something was an action, you have to find a way to make that action into a noun. For example:

The project was a failure due to lack of communication between team members.

The action in this sentence is "team members didn't communicate". But to put it in noun form, you say "lack of communication. You could also say:

The project was a failure due to team members not communicating.

In this example, "team members not communicating" acts as a noun.

a poor diet

"A poor diet" means not eating healthy things. You use the word "poor" to mean "not good" in formal situations in English, like when writing.

lack of (something)

"Lack of ___" means "not having" or "not being". You use this when you want to make a negative action into a noun:

A: I don't believe you.

B: Your lack of trust is understandable, but...