If the weight is from quantity, this usually happens because we got committed in more than God wanted us to (possibly in the past and now have the consequences).
If the weight is from very heavy things, it speaks of the necessity of yielding more consequences to God. We are in control of our choices and actions, but not of consequences. By our choices and actions we frequently attempt to make an outcome what we want, but we aren't really in control of it (otherwise we would always succeed).
In both cases leaning more on Jesus is probably necessary. Identifying the bare basics of what God has commanded you is a good first step. It is important to do a good job with these things. Step away from everything else, which typically can't be done instantaneously, nor does it necessarily produce short-term benefit. My experience is that only God can untangle our lives so we don't get caught up in something new when we get rid of some activity/commitment.
That some of what we do for enjoyment seems to help us through the days can make stepping away very hard. However, refreshment comes from the Lord, not from our choice of activities. Choosing to stop enjoyable activities so we can do better with what God sees as important moves God to grant strength and involves God to help in other ways, too.
A key fact is that being obedient to God makes God responsible for the consequences. Devoting more personal time to Jesus is beneficial in many ways, one of which is to make all the above more effective in the long-term, and probably in the medium-term as well. A regular habit of fasting will make a noticeable difference, possibly even in the short-term. Prayer and devotion time as well as Bible study always help over the long-term and sometimes noticeably in the short-term, too, since God blesses us through the power of his Word. One essential way God helps us is through knowing and believing his promises (and habitually asking for what you need and want).
By the way, you aren't carrying any weight on your shoulders alone. This is easier to experience by talking to the Lord about everything in addition to the other spiritual disciplines.