Are there large text-area fields in any of your models that are being queried on page load?

Joe has a good suggestion on something to check - any long text fields, or perhaps image fields that this user might happen to see larger values in? Could the page’s models return more rows for this user, if the user created or owns more records than others? 

Another thing you can try is to log in as the user, then open up the browser console and enter the command skuid.model.map(). Each model will be listed, and you can click on them to drill down and see lots of properties of each. You can also see the SOQL query that each model used. Try copying that query and running it in the Salesforce developer console. You should be able to see the full results of the query (without the heap size limit, I believe) and that might help you see anything that’s obviously larger for this user vs. others.

Also, you might compare the SOQL queries this user’s page sees, against those for an unaffected user. There could be a field set up in a model’s condition that’s meant to filter out some records, but this user can’t access that field, and the condition is therefore turned off.