"Come unto Me all you who labor and are heavy laden and I will give you rest." Matthew 11:28
The above words can be quite comforting once their importance is properly understood. In this question from Jesus we must ask, who does He mean? Who are bidden to come to Him so they may obtain rest?
Ask yourself, what is the greatest affliction of soul which sinners in this world experience? Is it not sin? Sin is the thing people labor under because it is a heavy burden and too great to carry by frail mortals.
Ask the mother who lost her dear daughter from a car crash if she ever labored under the sin of her own drunkenness? Or consider the gambler who spent his family's last $100 on a poker game in Las Vegas and couldn't afford to feed his children without going on a venture to steal from his neighbor. This is why Jesus calls to those who feel their sins as a heavy burden to come unto Him. Only by coming to Jesus can we find rest for our souls.
The world and the Devil try to trick us into finding rest by gaining more of this sinful world and more of the flesh, but this will only lead to death: "...for to be carnally minded is death, but to be spiritually minded is life and peace." Romans 8:6
The rich may be happy to have escaped poverty, but if they are like most sinners they are proud in heart because of their riches and so are an abomination to the Lord. Proverbs 6:5
The rich usually trust in themselves and their worldly wisdom more than their Creator who gives them the power to get wealth. These individuals seldom come to Christ because they do not labor and are not heavy laden. Some rich folks think too well of themselves. Many seem to know nothing that truly counts (like Godliness) yet they know how to get rich, and so pride feeds their brains and they fall under God's curse.
Poverty itself is no blessing, for it is possible to be poor in this world and also poor in the world to come. Many who are poor are tempted to steal, with fewer other means to provide for their security and living. In the final analysis neither poverty nor riches make a person fit for God's holy heaven, but rather a new heart, i.e. a new creation in Christ, 2 Cor 5:17.
Some think that those whom Christ bids come to Him are the physically sick and afflicted. I would believe this to be a misreading of Scripture since it does not seem to be the context. It is very possible to have physical trouble in this life and trouble in that to come. How is this possible? A person may be a kind of gypsy or wanderer in life despising material things and be no better off with the Master and Lord of Creation. He may be a lazy good-for-nothing sort of person who sees no value in work, but who likes to mooch off of the kindness of others. Poor health doesn't in itself merit favor with God.