The boy, since named as Ciaran Leigh Morris, was confirmed dead in hospital after the pram he was in was hit and trapped between a BMW and a wall in Brownhills High Street at around 4pm on Easter Sunday.
The baby was being pushed along the pavement by family when the BMW crashed into a Ford B-Max and then into the pram. A relative suffered a shoulder injury but nobody else was injured.
In an emotional tribute, Ciaran's parents said they were "happy we had the chance to meet you, look after you and call you our son".
Meanwhile a 34-year-old Walsall man has been charged with causing Ciaran's death. James Paul Davis is also accused of driving without insurance and leaving the scene of a crash.
As the community began to come to terms with the tragic events of the crash, members of the public laid flowers at the site on Monday and launched a fundraiser to support the boy's family.
Among those paying tribute was Kirsty Elkin, aged 30, from Brownhills, who said: "I think it is awful what has happened.
"I walk down (the road) loads with my dogs. I felt compelled to place flowers here.
"I don't know the people but I have got a seven-year-old and a four-year-old. It is heartbreaking.
"My thoughts are with the family. I cannot begin to imagine what they are going through."
Cards, toys and teddy bears were among the tributes at the scene, where damage to a brick wall could be seen next to Nannza Pizza and Retribution Tattoo.
Shaun Helay, head coach at the nearby Walsall Wood boxing club, laid a red boxing glove amidst the flowers, with a message which read: "RIP... Little man from all at Walsall Wood Boxing Club. God bless your family."
Mr Helay, 59, from Rushall, told the Express & Star: "We all feel sorry for them. We want to do something for them and raise money for the parents."
Jamie Robinson, 30, from Brownhills, who lives nearby, also placed flowers at the scene, and said: "It made me feel sick, it should not have happened.
"I could hear the sirens and the ambulance helicopter come over. The child was so young."
One of the flowers, placed by somebody else, had a heartfelt message written, on which said: "If only, little one, we could send a basket filled with love, and pretty blue forget-me not's to your new home above.
"If only we could send a hug past every twinkling star, and a suitcase filled with kisses up to heaven where you are.
"If only you could be rocked as you were not long ago and sung one more lullaby before you had to go.
"If only's fill peoples every thoughts as their hearts are aching for you.
"With faith, they'll wait until the time "if only's" all come true.
"Rest easy little one - sending love to your mummy and daddy."
A fundraising page set up to raise £2,000 to support the boy's family had raised more than £2,900 by mid-afternoon on Monday.
Karl Roberts, who launched the page, wrote: "On the 4th of April, a traffic collision occurred on Brownhills high street that resulted in the loss of life of a two week old baby. We are trying to raise funds to support the family at this very difficult time."
To donate visit justgiving.com/crowdfunding/brownhills-rtc-04-04
Sergeant Mark Crozier, from the collision investigation unit, said: “A baby has tragically died and we’ll be doing all we can to support his family during this deeply devastating time.
“We’re in the process of speaking to witnesses and establishing the circumstances around this collision.
“I would ask anyone who was in the area, and has information which can assist our inquiries, to come forward.
“We understand the shock this will have caused but I would ask people not to speculate on what happened.”
Anyone with information can contact police via FL_COLLISION_INVEST@west-midlands.pnn.police.uk, via Live Chat or by calling 101.