Firstly, is this right?:

Exothermic reactions have a negative enthalpy change value because the enthalpy of the reactants are greater than the enthalpy of the products *since the reactants have weaker bonds.*

(especially the starred part, I'm wondering about)

If so, how come weaker bonds means higher energy/enthalpy?

My personal take on this is that you are "worrying this point to death". I look at it this way.

When (n*dH products) - (n*dH reactants) = - number, we have an exothermic reaction and it gives off heat. When the number is + it is an endothermic reaction and it absorbs heat. I don't know that it says anything about which bonds are stronger and/or which are weaker.

Yes, your statement is generally correct. Exothermic reactions are characterized by a negative enthalpy change because the enthalpy of the reactants is greater than the enthalpy of the products.

Now, let's dive into the starred part of your question. In a chemical bond, atoms are held together by the attraction between their positively charged nuclei and negatively charged electrons. The strength of a chemical bond determines the amount of energy required to break that bond. Stronger bonds require more energy, while weaker bonds require less energy to break them.

When it comes to energy and enthalpy, it is important to understand that energy is released when bonds are formed and absorbed when bonds are broken. In an exothermic reaction, the reactants have stronger bonds compared to the products. Breaking these strong bonds in the reactants requires more energy than is released when new bonds are formed in the products. Therefore, the overall enthalpy change for an exothermic reaction is negative because more energy is released (given off) than absorbed.

So, to summarize, weaker bonds in the reactants mean that less energy is required to break these bonds compared to the energy released when new, stronger bonds are formed in the products. This leads to a negative enthalpy change, indicating an exothermic reaction.