Before you do anything be sure the seacock is in good working order!
How old is the hose? Hoses are a maintenance
item, and since the galley drain gets grease (oil is a solvent), boiling water, and various chemical concoctions (cleaners, acids (vinegar, lemon juice) alcohol...) through it on a regular basis, it is a good idea to renew that hose every five years. When you remove it you will find out if a clogged hose was the problem.
While the hose is off, put a bucket under the drain and pour some water through to see how fast it drains - that should tell you if you really need a larger sink opening. Next, put the new hose on the drain and run the other end to the bottom of the bucket and fill the bucket 3/4 full of water - try to position the bucket so the top of the water in the bucket is near the waterline of the boat, and to do a really good experiment
place the bucket so the run of hose to the bucket waterline is similar to how it would be if the hose were attached to the seacock. If it is slow draining then a vent line may be the solution.
Quite a few boats have the bottom of the sink near the waterline, (some have to be pumped out because they are below the waterline), and the "solution" for that is the gray water tank and pump - "solution" because of what could grow inside that tank, not to mention the smell.