Of course deductions carry scientific weight, but they don't serve as meaningful evidence and instead as the basis of a hypothesis.
Genuinely logical deductions carry equal or greater weight as experiments. Logical deduction is part of the process of scientific analysis. Logical deduction is in fact the glue that connects otherwise disconnected scientific theories. Without logical deduction, scientific theories would be disconnected semantic dust.
Without the rules of math and logic, you can't do scientific analysis. Experiments are the data, logic and math are the engine. Its logic that tells us if the Earth is spherical its not cubical. No one does experiments to prove the Earth is not every other possible shape. Its logic that tells us that if the Earth has one shape, it cannot have another. No experiments are necessary. No one has tried to experimentally confirm the Earth is not a dodecahedron, or a torus, because those are logical impossibilities.
You are probably confusing genuine deductive logic for what people sometimes call deductions but are actually inductions or "common sense." Those typically fail often. But they are not true logical deductions. "Holmesian deduction" is not generally real logical deduction. But when you say science uses experiments to support a conclusion, on what basis do you declare those experiments support anything? Why does seeing X support Y? Without logical deduction, you can't get from here to there. Experiments don't tell you that X supports Y, experiments generate the X. Logical deduction connects X to Y. It is in fact two logical deductions that underpin two of the foundations of Science. If an assertion always leads to X, and an experiment demonstrates that X is false, then the original assertion cannot be entirely true. That's the principle of falsification. Conversely, if an assertion predicts a set of circumstances S, and the set S is distinct from all other similar assertions, then if experiments confirm all the elements of S, the probability that the original assertion is true increases with the size of S. That's the principle of confirmation. Try and do Science without variations of those deductions.