Weissman started his career with hometown club, Maccabi Haifa. In January 2014, Weissman made his first-team debut in the Israeli Premier League match against Hapoel Be'er Sheva. He came off the bench in the 79th minute, replacing Ran Abukarat. He ended the season with 10 league appearances, while only appearing in two games in the following season.
2015–18: Loan spells
On 19 August 2015, Weissman signed for fellow Israeli Premier League club Hapoel Acre on a season-long loan from Maccabi Haifa. After scoring no goals in 18 appearances, the loan deal was cancelled in January 2016. For the 2016–17 season, Weissman was sent on a season-long loan again, this time to second division club Maccabi Netanya. He managed to score 12 goals in 21 league appearances, helping Maccabi Netanya achieve promotion to the Israeli Premier League as they were crowned champions at the end of the season. In the following season, Weissman made one appearance for Maccabi Haifa before being sent out on loan once again in August 2017, this time to fellow Premier League side Ironi Kiryat Shmona. In September 2017, in a league match against Ashdod, Weissman scored his first goal on the highest level of Israeli football in a 2–0 win for Ironi. He made 26 league appearances for the club, scoring three times.
2018–19: Return to Maccabi Haifa
Following the expiration of his loan, Weissman returned to Maccabi Haifa. He made his first appearance in the season as a substitute in the league match against Maccabi Tel Aviv on 26 August, receiving a yellow card shortly after in a 0–2 loss. A few days days later, on 1 September, Weissman scored his first Maccabi Haifa goal when he netted in a 2–0 home win over Ashdod. He ended the season with eight goals in 25 league appearances.
Wolfsberger AC
On 20 June 2019, Weissman joined Austrian Football Bundesliga club Wolfsberger AC, signing a two-year contract and being handed shirt No. 9. On 17 August, in the fourth round of the league, Weissman scored four goals in a 5–0 home victory over SV Mattersburg. Before the match, he had scored in three consecutive league appearances for the Carinthian club. On 19 September 2019, Weissman scored the first goal in a 4–0 win over German club Borussia Mönchengladbach in the Europa League group stage, Wolfsberger AC's first European goal ever. He finished the 2019–20 season with 30 league goals which made him the Austrian Bundesliga's top scorer.