Well, this might be a case of the question answers itself. If the item is too heavy for the crew to be pickup it will be left and noted on their DS350(which is the card they have to note anything that happens on their assignment for that day), simple as that.
Now what happens after that is the tricky part. At one time the section officer would make arraignments to have it picked up after contacting owner of said garbage.
These days a field officer is only there for the day and might not know what happen and it might get overlooked.
If item stays out there overnight, you might get a summons for putting out collection on wrong day (it’s possible).
This is the best thing to do!
Break it up into smaller size items and put back out for collection. Rule of thumb is if it’s too heavy for you to pick up its probably too heavy for me to pick it up.
Caution: To avoid extra stress and headache call 311 and tell them of the miss collection and get a complaint number from them, just in case you are issued a summons for leaving garbage out or just take item back in away from the curb until your next collection and breaking it into smaller items.