If you don't have a tool like DynaTrace, maybe you can collect some trending heap histograms for analysis in pandas?

trending_histogram_heap_dumps.sh

#!/bin/bash
[ -z "$PROJECT" ] && PROJECT=LitWR
[ -z "$HOST" ] && HOST=$( hostname )
[ -z "$PGREPEXPR" ] && $PGREPEXPR="Xdock:name=Minecraft"
sleep 10
PID=$( pgrep -f "$PGREPEXPR"|head -1 )
while [ x != x$PID ] && [ "0$(pgrep -f "$PGREPEXPR"|head -1)" -eq "0$PID" ]
do
  jcmd $PID GC.class_histogram > ${PROJECT}_$( hostname )_${PID}.Histogram.$( date +%Y%m%d%H%M%S ) 
  sleep 10
done

ls ${PROJECT}_${HOST}_${PID}.Histogram.* |
  sort -n |
  awk '{n=split($0,array,"."); printf("%s %s\n", array[n], $0 ) }'|
  ( while read dt f
      do
        export dt
        awk '/[0-9]:.*[0-9]/ {printf("%s,%s,'"$dt"'\n",$4,$2,$3)}' < "$f"
      done ) |
      ( echo ",classname,instances,bytes,timestamp"
        i=0
        while read csvline
        do
          echo "$i,$csvline"
          i="$(( $i + 1 ))"
        done
        ) > ${PROJECT}_${HOST}_${PID}.csv