For the flight from Grand to Little and back - they will weigh your total checked bags and they can not total more than 55 lbs. The carryon bags will be weighed as well and can not total more than 15. How strict they are depends on the agent that checks you in. If you are over, they CAN charge you per pound but it is quite inexpensive.
The overweight charge (above 55 lbs including carry-on) may be waived or not, but it is usually pretty cheap. Whether or not they will charge you seems to vary with how much other stuff has to go on the plane. I do recall that the last time we were on LC that a guy on our plane paid something like $80, but he had loads of gear and camera equipment.
You won't be allowed any large carry-ons (no rollerboards or large back packs, etc.) because large carry-ons will be placed in the baggage hold. There are no "overhead bins" on the small Twin Otter planes.
It's not unusual to have a bag delayed for a day. This is a bigger problem for Little Cayman because Cayman Brac has a larger airport that can accept bigger planes and even jets both day and after dark. The small airport on Little Cayman can only take small propeller planes and only during daylight.
The last time we were there the suitcase with most of our clothes was delayed for a day. The staff at the LCBR laundered our clothes for free to help us get by until our missing bag arrived. A couple on our boat had the bag with all their dive gear delayed - but the dive shop loaned them gear for free until their stuff arrived. I tend to bring a large, soft purse that I can jam under the tiny seat in front of me and I pack it only with essentials like medications, glasses and contact lenses, money, credit card, C-cards, swimsuits, clean undies, and phones and dive computers, just things that we will really need if our luggage is delayed.
If you are staying at LCBR, and you enjoy a few cocktails while on vacation, did you buy a drinks package with your hotel/food/diving package? If yes, then you will be able to choose up to 3 drinks per day (well drinks or soft drinks) at no charge. If not, be aware that the drinks at the bar are rather expensive and a 15% tip will be added to anything you purchase, even just a can of Coke. But you probably already know this because I think that you've previously stayed at a Clearly Cayman resort(s), correct?
Each adult can bring a liter of liquor into Cayman duty free, you can buy it at the duty-free shop at the airport before you leave the US - but be aware that if you are continuing on to one of the Sister Islands, you will have to go through Security at GCM and they will confiscate the bottle if you try to carry it on with you because it is larger than 3 oz and doesn't fit in a zip-lock quart bag. You have to pack the bottle inside your luggage before re-checking your bags for LC and then go through Security - and it will of course be counted in the total 55 lbs weight allowance.
I haven't been to LCBR since all the remodeling, but there used to be an ice machine near the bar that guests can use. You can buy mixers at the resort or in the grocery store in nearby Blossom Village. That store was open on Sundays when we were there, unlike many other stores in Cayman.
How long is your layover at GCM before traveling on to LCM? If you have time, after you check your bags but before you go through Security, grab the free shuttle to the nearby George Town Yacht Club. You can enjoy a nice meal in a lovely setting, see link below. The meal package at the LCBR starts with dinner the first night, so it's nice to have lunch on GC (or breakfast on the way home) but if that won't work for you, then you can buy lunch at the beach bar at the resort. (Or in the departure lounge at GCM, not a thrilling prospect!)
George Town Yacht Club
When are you traveling? LC pretty much shuts down from August through October, see the link below. The LCBR stays open as does that little store in Blossom Village that I mentioned (I think that it has the only gas pump on the island) but the Hungry Iguana Restaurant and most other places on the island will be closed for the summer.
You can borrow a bicycle from the resort or walk to Blossom Village; or rent a car for a day or two to check things out if they will be open. The hotel will arrange the car rental for you. The Central Caribbean Marine Institute offers tours on Friday and there is a small museum in Blossom. You can also rent kayaks and go over to Owen Island to snorkel.
https://www.caymancompass.com/2015/08/07/little-cayman-s-big-summer-shutdown/
Damian, a former bartender at the Beach-Nuts Bar at the LCBR, now operates a glass-bottom boat and offers tours, fishing, and other water excursions; including excursions over to uninhabited Owens Island to snorkel or fish, see the link below. I don't know if he stays open during the summer.
Restored glass-bottom boat now Little Cayman tourist vessel | Cayman Compass