A little digging through logs, and taking a "how to get it working with, even if not fully supported" approach. It looks like flyweight tasks are getting prioritised as per rules in http://jenkins_host:8080/jenkins/advanced-build-queue/
Heavy weight tasks on the other hand (where prioritisation would be really useful) look to be hitting PriorityConfiguration.java#L211-L216 and so getting assigned a default value.
Can we ease

if (!(item.task instanceof Job)) {

That way we could atleast add filters to re-prioritise

Code changed in jenkins
User: Oleg Nenashev
Path:
pom.xml
src/main/java/jenkins/advancedqueue/PriorityConfiguration.java
src/main/java/jenkins/advancedqueue/PriorityConfigurationPlaceholderTaskHelper.java
http://jenkins-ci.org/commit/priority-sorter-plugin/14df308bde82d46cd255ff777f9aaf4b3c13f06b
Log:
Merge pull request #34 from vitalii-vitrenko/master

JENKINS-36570 Implement pipeline compatibility

Compare: https://github.com/jenkinsci/priority-sorter-plugin/compare/5e5657d7d246...14df308bde82

https://github.com/jenkinsci/priority-sorter-plugin/pull/34 adds some bits of the Pipeline support, but it is not a final solution.

Job property handling needs to be reworked and updated

Code changed in jenkins
User: Oleg Nenashev
Path:
src/main/java/jenkins/advancedqueue/PrioritySorterConfiguration.java
src/main/java/jenkins/advancedqueue/jobinclusion/strategy/JobInclusionJobProperty.java
src/main/java/jenkins/advancedqueue/priority/strategy/PriorityJobProperty.java
http://jenkins-ci.org/commit/priority-sorter-plugin/c9bfe6d16a2f34e1e184e448f1f8ac6329be531c
Log:
JENKINS-36570 - Cleanup references to AbstractProject in the core plugin classes

Generally this change is not binary compatible, and likely it requires 4.0

Code changed in jenkins
User: Oleg Nenashev
Path:
src/main/java/jenkins/advancedqueue/PrioritySorterConfiguration.java
src/main/java/jenkins/advancedqueue/jobinclusion/strategy/JobInclusionJobProperty.java
src/main/java/jenkins/advancedqueue/priority/strategy/PriorityJobProperty.java
http://jenkins-ci.org/commit/priority-sorter-plugin/f74d95fc13f4c17a4ab998846c4b087e6befc077
Log:
Merge pull request #36 from oleg-nenashev/JENKINS-36570-AbstractProject-cleanup

JENKINS-36570 - Cleanup references to AbstractProject in the core plugin classes

Compare: https://github.com/jenkinsci/priority-sorter-plugin/compare/14df308bde82...f74d95fc13f4

I see that this is now merged in, but could anyone say to what extent this is useful in practice, and how to use it, as it wasn't obvious from this issue and the PR

Dominic Hargreaves I've though the existing documentation is enough. What exactly you're interested in? The plugin itself or it's Pipeline integration features?

Code changed in jenkins
User: Oleg Nenashev
Path:
COMPATIBILITY.md
http://jenkins-ci.org/commit/pipeline-plugin/615a0b9b0c3ade0157da4cd8118398b608a1e679
Log:
JENKINS-36570 - Add PrioritySorter to the Pipeline Compatibility list

Code changed in jenkins
User: Jesse Glick
Path:
COMPATIBILITY.md
http://jenkins-ci.org/commit/pipeline-plugin/db5cf31926d7e009cf30ed14a8e7325d384067e9
Log:
Merge pull request #428 from oleg-nenashev/PrioritySorter

JENKINS-36570 - Add PrioritySorter to the Pipeline Compatibility list

Compare: https://github.com/jenkinsci/pipeline-plugin/compare/74522f80f474...db5cf31926d7

Oleg Nenashev I had a look at https://wiki.jenkins-ci.org/display/JENKINS/Priority+Sorter+Plugin and the only mention of pipeline is a change entry mentioning this ticket. But I can't see anywhere how one would allocated a node in a given job group, which I assume is how this would need to work, any examples at all of it being used in a pipeline script. So given your reference to existing documentation I suspect there's something I'm just not finding from a google search?

I was probably coming at this from the wrong direction. I can confirm that job groups/priority sorting works on a pipeline job as a whole and that is good enough for us at the moment.

Dominic Hargreaves There are some bits with Pipeline compatibility, e.g. JENKINS-44014

But I would rather say the plugin is compatible though there is not enough documentation. If you could note your findings somehow, I could put them to Wiki/GitHub