The highway from Ipswich to Rodway is currently overcrowded with traff

Good analysis! However premise clearly states that "congestion is deterring potential customers from visiting Rodway's stores". As premises are considered true, we cannot weaken them. We can weaken the logical reasoning or the link between premises and conclusions or the conclusion itself. So, as per your analysis, only one weakening option remains: "or it will say that widening the roads won't save the stores, which are struggling ". Considering this, correct/incorrect choices become more evident.

My take on option C is:

Premise states that stores in Ipswich are thriving since the road between Ipswich and Martin was widened. (NOTE: no mention of Martin's stores in the premises)

Option C states that Martin's residents have much more purchasing power than Ipswich's residents. This implies that since the road between Ipswich and Martin was widened, Martin's residents were able to reach and purchase at Ipswich's stores, thus increasing Ipswich's stores' revenues. This in fact reinforces the premises, and hence actually strengthens the conclusion, that is based on a positive relation between widening of road (thus reducing congestion) and stores' revenues.

Having ruled out option C, E remains.
Conclusion: Widening Road => (alleviate congestion) => Increased Revenue of Rodway's stores

E states that widening of road didn't have a significant effect on Martin's stores, thus there is no reason to believe that widening of road will have a significant effect on Rodway's stores.
In short, option E is: Widening of Road --Not Always--> Significant Increase in Revenue

In cases of cause and effect, If A causes B, i.e., A->B, then this relationship is considered strict and binding. In all cases A should cause B, and to the same extent. E clearly weakens this causal relationship as stated in the argument, hence should be the answer.

Option D is out of scope as it doesn't refer to the reasoning used in the argument and states extraneous factors (such as advertising, merchandise etc.) that may or may not affect stores' revenues.