Despite trailing their hosts by seven points Slovakia could reduce their rivals' advantage with successive victories.
They begin the task in Zenica on Friday before hosting the return game in Zilina on Tuesday.
"The Bosnians have one foot there (in qualification) but we have two games with them," said Weiss.
"We can get six points and torment them. They too will have respect for us and it will be an interesting match, although it will not be easy.
"Bosnia have a good team and they play football very fast but the chance is still there and we have a great team.
"We show that when we combine as a collective."
Bosnia coach Safet Susic is confident his side will be able to hold off the challenge and at least maintain the gap over their third-placed opponents.
"I know it will not be easy but we have a better team, playing in front of their own crowd and expect to win," he said.
"I know that they need to beat us so I expect an open game with plenty of chances and goals.
"You'll see that tomorrow's team is one of the best in the world: we are the best in terms of knowledge and techniques and when we add grit to that I think there should not be any problems."
Bosnia need at least a point from the game to ensure they are not overtaken by Greece, who travel to bottom side Liechtenstein.
The Greeks will be big favourites to claim three points against the group minnows but will be wary of a team side who have managed to claim draws in their last two qualifiers against Latvia and Slovakia.
A win for Greece coupled with a loss for Slovakia would effectively secure at least a potential play-off spot for Fernando Santos' men with a home game against Liechtenstein to come in October.
Liechtenstein boss Rene Pauritsch goes into the game with five of his players on yellow cards and is hoping they can keep their cool with three more qualifying games to follow.
"We are hot headed," he told Liechtensteiner Vaterland. "We need to estimate the value, then we can decide.
"The midfielders at high risk with the yellow cards must be careful but still battle.
"We have to be careful about how to solve the matter."
Latvia are looking to move ahead of opponents Lithuania in the group's other fixture, although qualification for either is virtually unobtainable.