All that molar weight (or molar mass) tells you is how many grams of something are in 1 mole of that thing. That's what atomic masses are on the periodic table- so Calcium weighs 40 grams per mole, Carbon weighs 12 g/mol, etc.
One thing to recognize is that 1 mole of AB = 1 mole A + 1 mole B. Why? Say I had some bags of fruit, and each bag contained 1 apple and 1 orange. If I gave you 100 bags, you would have 100 apples, and 100 oranges, not 50 and 50.
Similarly, If I say I have 1 mol HCl, that means I have 1 mol H + 1 mol Cl:
1 mole H at 1 gram/mole = 1g
1 mole Cl at 35 grams/mole = 35g
In total, 1 mole HCl = 1g + 35g = 36g
So, HCl weighs 36g/mol.
For your example, just follow the same procedure: break it down, find the individual molar masses, and add them back up.
In 1 mole of CaCO3, you have:
1 mole Ca at 40 g/mol = 40g
1 mole C at 12 g/mol = 12g
1 mole O3 at (16 x 3) g/mol = 48g (because O3 weighs 3x as much as O)
1 mole CaCO3 = 40g + 12g + 48g = 100g.
So, the molar mass/weight of CaCO3 is 100 grams per mole, or 100 g/mol.
Hope this helped!