Dreadhorde Arcanist allows you to "cast target instant or sorcery card with converted mana cost equal to or less than dreadhorde arcanists power from your graveyard without paying its mana cost" but for cards with overload costs that state in it's own separate ruling that we "may" cast it for its overload cost, can I use dreadhorde archanist to reach and have the ability to cast a card like "weapon surge", then choose to pay its overload cost for its overload effect?
No, you cannot pay the overload cost for spells cast that way.
Dreadhorde Arcanist allows you to cast a spell with an alternate cost of "without paying its mana cost". The Overload ability also defines an alternate cost. You can only use one alternate cost when casting a spell, and if you are casting a spell using Dreadhorde Arcanist then using that alternate cost is mandatory.
No. From the card rulings on gatherer:
If you cast a card “without paying its mana cost,” you can’t choose to cast it for any alternative costs.
Overload is an alternative cost (not an additional cost):
702.95a Overload is a keyword that represents two static abilities that function while the spell with overload is on the stack. Overload [cost] means “You may choose to pay [cost] rather than pay this spell’s mana cost” and “If you chose to pay this spell’s overload cost, change its text by replacing all instances of the word ‘target’ with the word ‘each.’” Using the overload ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.