This works quite nicely in an iframe. Particular settings (layers, location, zoom) can be saved using the Save/Share button at the bottom and plugging that into the "src" attribute of the iframe. E.g. I just quickly stuck this into a otherwise content-free page and got it to work first try:
<iframe style="width: 100%; height: 70vh;"
src="https://preview.weather.gov/edd/?lat=42.3492&lon=-72.0173&zoom=6&ql=TFFFFFFFFFFFFFFFFFFFFFF&ml=U.S._States|520|0.8&bm=ESRI_Dark_Gray&lsr=F&lsrp=3&lsra=&mp=F&lfc=F&rt=Observed&rf=status='major' or status='moderate' or status='minor' or status='action'&ht=threat&pid=N0Q&sf=GOES_Infrared_-_SSEC&ri=5&obs=TFTTFFFFFFTF&is=1&ou=mph&od=-50&ships=F&cluster=T&radO=0.75&satO=0.75&hazO=0.3&tropO=0.7&ndfdO=0.7&ndfdR=Continental_US&ndfdF=Maximum_Temperature_(ºF)&ndfdT=12&ndfdTS=&lviz=F&fullscreen=F&fxt=Point_(Text_Only)&ppd=24&pdy=3&satf=60&obsync=F&flavor=Advanced&tfo=null&tfd=null&tfw=null&ht=F&hd=F&ho=null&hf=null&hb=F&hsps=F&ot=Meteorological_Observation&hvt=F&sht=F&ehm=T&uwl=F&ec=F&lll=F&keys=&ofont=14&opnt=1.2&oset=15&oan=F&oap=1&oid=F&cc=Pub&oo=F&cs=F&rs=P&ofbs=">
</iframe>
Pretty cool...