Is there any equivalent for this Persian proverb "A lopsided load won't reach the destination"?

Something that has equivalent connotations of "you did something bad and now you have to (or soon you will have to) deal with the consequences":

You reap what you sow:

everything that happens to you is a result of your own actions.
If you treat your friends like that, of course they drop you. You reap what you sow in this life.
_{source: TheFreeDictionary.com}

It isn't a proverb so much as an idiom, but I will offer cheaters never prosper or sometimes just cheats never prosper.

If you cheat people, they will not continue to do business with you, and so your business will fail.

I am most familiar with this as a playground taunt among elementary school children- when one of us would try to bend the rules at dodge-ball or red-rover, the others would call him out and chant "Nah-nah-Nah-nah-Nah-nah! Cheaters never prosper!" It is also used in many other situations, however, and has a similar meaning to what you describe.

Reminding someone to stay on a/the “straight and narrow [path]” is similar to cautioning someone to straighten their lopsided loads, not in the sense that a lopsided load will eventually topple, but that it won’t fit on the narrow path or through the “strait” gate leading to whatever rewards might await those who live good and honest lives.

straight and narrow noun: informal the proper, honest, and moral path of behavior
[perhaps an alteration of strait and narrow, an allusion to Matthew 7:14: 'strait is the gate, and narrow is the way, which leadeth unto life']

(from ‘Collins English Dictionary’ via ‘The Free Dictiobary by Farlex’)

Your edit mentioning “Honesty is the best policy” (which although capturing the essential meaning of the original, is arguably a bit too general) prompted a search for other idioms containing “honesty” that, unlike "Honesty is the best policy," specifically include the notion of motion on a path toward a desired destination.

The following is the only one I found containing a direct mention of motion, but unfortunately it appears to have been concocted by Ed Shewan and Annie Lee Sloan, the authors of ‘Mastering Communication Skills’ merely to provide an example of a simile, for it is not at all familiar to me and more importantly, is found nowhere else on the internet:

Dishonesty breathing in a heart is like a bicyclist going downhill without brakes.

(from ‘Google Books’)

There is the following quote (attributed by some to Mark Twain), however, that is legitimate and fairly well-known and which could be paraphrased to kind of include the notion of “staying on [the right path]” by using “stick to” or “stick with” instead of the quote’s original (or close to it) phrasing:

Speak the truth at all times, it's easier to remember.

(from ‘Here's How: An Introduction to Practical Discipleship’ by Lee Brown, via ‘Google Books’)

Paraphrasing it with “stick with” would give:

[Always] Stick with the truth, it’s easier to remember.

(from ‘Family Matters: An Ernest "Sparky" Hemingway Mystery’ by Joel Rosenberg, via ‘Google Books’)

and paraphrased with “stick to”:

[Always] Stick to the truth, it’s easier to remember.

(from ‘One Day Too Long: Top Secret Site 85 and the Bombing of North Vietnam’ by Timothy N. Castle, via ‘Google Books’)

I would say that a similar proverb is what goes around comes around:

A person's actions, whether good or bad, will often have consequences for that person.

[Wiktionary]

This essentially says "a lopsided load won't reach the destination," but also implies that a balanced load will.

Also, you could say karma's a bitch, which has essentially the same meaning.