As per the PHB.154, smithing tool's will weigh 8 lbs. I would assume it doesn't include an anvil (the lightest of which come around 75lbs according to Google.), and the hammer itself would weigh a few pounds. This leads me to assume a smithing kit is only the most basic of tools.
Additionally, if you wish to keep your character's load capacity in check, you could enforce encumbrance rules. At a strength of 16, maximum carry weight would be 240lbs (STRx15), and light encumbrance would be felt at 80lbs( 33% load capacity). A weight between 80 and 160 (33%-66%) would reduce movement speed by 10. Between 160 and 240 (66%-100%), your movement is reduced by 20 and you have disadvantage on ability checks, attack rolls, and CON/STR/DEX saves.
When determining what might be overkill, it's important to recognize a few things about relative weight. A 2hand Maul weighs 10lbs, while a heavy xbow weighs 18lbs. This may seem like a lot, but scale mail and half plate are about 40lbs each, while Chain, splint, and plate are 55, 60, and 65lbs respectively. A handaxe and dagger are 2 and 1 lbs. In total, plate armor+Maul+xbow+handaxe+dagger comes to 96lbs. If your player's strength is less than 18, you could impose a movement penalty. This is before considering the weight of other misc items he may carry, as well as the weight of gold.
Overall, I would say the equipment loadout is fine. For a weaker character, the loadout would be a great strain. For a strong fighter-type character, it would be a regular load.