The aircraft shown in the picture is a Cessna 402 flown by Cape Air. Their official baggage policy for such aircraft is similar to WW.'s experience; I've emphasized the pertinent text in the quote below. There also appears to be a hard upper limit on the weight of "overweight" bags, as well as limitations on oversized items (i.e., don't bring 'em.)
For each ticketed customer, Cape Air will transport:
1 checked bag not to exceed 50 lbs or 62 linear inches plus 1 gate checked bag not to exceed 45 linear inches plus 1 personal item (e.g. small purse, briefcase, laptop) not to exceed 36 linear inches. These aircraft do not contain storage space under the seat or overhead in which to safely stow in-cabin items. Accordingly, personal, or carry-out, items must be carried to the aircraft and stowed by a Cape Air agent into the designated baggage compartments prior to boarding. ...
For each ticketed customer, Cape Air will transport, subject to available space and additional fees up to two (2) additional bags per passenger. ...
All excess baggage is carried on a space available basis and is subject to an additional charge.
Baggage compartment constraints of the aircraft may restrict the weight or the size of the individual bags that may be accepted for travel. Baggage that is not accepted for travel pursuant to this section is as follows:
Individual bags that exceed 70 lbs in weight or that exceed 62 linear inches in size. ...
Bicycles, surfboards, canoes, kayaks and other such large pieces of sporting equipment exceed the capacity of the compartments and are not accepted for transport. ...
It is not permissible to transport cabin baggage in any aircraft by strapping the item to a passenger seat.