The "Restrained Weight" case sets the design load, hot or cold. That can be considered the balanced load.
Let's assume the pipe grows up from hot to cold. Then, for (default) hot load design, the hot load will be set by that "Restrained Weight" case and that same spring must also carry the LARGER cold load. For cold load design, the cold load will be set by that "Restrained Weight" case and that same spring must also carry the SMALLER hot load. These two approaches may pick the same spring but they need not be the same.
The question, then, is, when should this support be "balanced"?
Of course a little human intervention may be necessary to tune things up.
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Dave Diehl